Introduzione alla filosofia della matematica

176 Pages·2018·3.084 MB·Italian

by  Matteo Plebani

STUDI SUPERIO/RI6 44
FILOSOFIA
A MarBiaae tzing
Evei/nt hewreern eon umbers,
givmeey ouph ro nneu mebr
Il etcthodere is iderano
informsauvzioi lounmii
pubbldiaclcalataesi da i trice
possroinvoo ldgierrestita a:m ente
Caroecdciit ore
CorVsiot tEomrainouI eI2l,2e 9
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teleof64o 2n8I o 8 4I7
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Siamo
su:
htpt://wcwawr.o ctc i.i
htpt://w ww.faceboocka.rcoocmc/i editore
htpt://wtwwwi.t ctoemrc/.a roccieditore
MattePol ebani
Introduzailolfnaie l osofia
delmlaat ematica
Caroecdciit ore
ra ristamp2a0,18 giugno
ra edizliuog2nl0eIi,Io
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Riproduvziieoatnsiaee t nads ii legge
(a1r7t1d. e llleag2 2g aep r1i9l41ne,. 6 33)
Senrzeag oaluatroer izzazione,
èv iertiaptroo qduuervsrotelo u me
ancphaer ziaelc moqenun atlems ezizaos,i
comprlefaos otac opainacp,he eur s ion terno
od idattico.
Indice
Premessa 9
Ontoloing uimae:er sii stono? 13
L
Dic ospaa rliamo quanddieo s ipsatrelnizaam?o 14
LI.
1.2.O ggetti mavtso egmgaettitdcieivl milatatà e matica 21
1.3.D omanfdaec eid loim anddief ficili 29
1.4.L av isidoiCn aer ndaepl l'antologia ... 30
1.5.. .e. s iu opir oblemi 33
r.6.T rael ternema etzizvoe 35
r.6D.urse.e ndseqilu antilfir c.a6Et.so2ir.se et m eentzaalf ora
r.6L.'3e.r esia mlre .i6Ln.aor4 ne.ga èhl itoaàpn ear atore
un
1.7.A rgomepnetiripl l atonismo 46
r.8.L av idaiQ uine 48
r.8L.'1a.r godmQie uniltn1 oe. 8L'.a2r.g omdeiinn tdoi s-pensa
bill1i .t8àL. '3a.r godmiBe unrtgoeR soss een
1.9.L av ifar egeana 62
1.10N.o mianlismi 65
II.I . In osatnrti engaotoid maniani 67
1.12C.h ihalrapa o:s sibdiill aistcuàin a rsee cgonnoc reto 72
1.13F.i eclhdce:o ssaip roavdae sseurnne o minalista 73
1.14D.ac hpea rsttea re? 78
2. Metaficshiec ac:o sian usmoenroi ? 83
2.1.L' ereddiiFtr àe ge 84
7
2.2.Q uattvrioe 86
2.3.N umeeri in siemi 89
2.3C.1h.ce o sun 'ièn sile2 m.3e.C?2o. n frcoonlntma oe reolo-
gil2a . 3Q.3u.e lclhioen umenropino sseosnsoe re
2.4.St rutturalismi 104
2.5.A strazvieocnceihn iueo ve 109
2.5.I1pl.i pùr egnparanatgoerf laiofiscodofit utitt meip li
2.5.I2pl.r obldeiCm eas are
3· Epistemocloomg'pièoa s:s icboinloes gcleoirg eg etti
matematici? 119
3·1.C onoscfeannztaa sma 119
3.2.L' argomedniBt eon acerraf 120
3··3 Lav ersiaogngei ordniFa iteal d 126
3-·4 Critiaclhle' argdoiFm ieden !t o 128
3·5·L ogiecm aa tematica 134
3.6.li platondieslmploia e nezza (Balaguer) 135
3·7·L at ecshile am atemaètl iocgai ca 143
3.8.C omef acciaas maop ecrhee( HPè)v ero? 151
3·9·C attciovmep agnie 154
3.10M.a tematliocgaiem,c o ad alità 156
3.11O.g gemtattie mavtso igcgie ttdievlmilatatà e ma(tIiIc)a 157
Bibliografia 163
Indidceneio mi 173
8
Premessa
Lam atemasteiccoan,ad loc uènl iar, e gidneals lcei eDnizc ee.r pteoir
filohsaso efim prraep presuennsatc aiteomn ozlati on terespsevarin at e,
diq uelclheea ,il orooc chsio,na op pacrosmece a rattedreitlsu ttitcoh e
peculiari.
Peprr imcao sla',o ggdeist ttuodd ieolm laat emartiiscudali tvae rso
daq ueldleola llets rcei efnizsebi:ic oal,eo c ghiiam siecmab racnoomn,e ­
todeni o zidoinvie irnsdea,g iamlro en dfoi silcam oa;t emavtiicceav,e r­
sat,r attdainn udmoe fruin,z iionnsii,eec moisv ìi paa,r aev earc hfea re
conu nm onddoio ggeatsttir ea,qt utail unsqiiuasle i gnifdiiqc uaet­o
st'aggceitsòte imvbocr,oa n feurnir rulodele otl u tstpoe cilacil aesd.oe l­
lam atemartaipcpar elsaes nfitdpaai gùr anpdeecr h iunvqougels ioa­
stencehrseeo limolo nddoe golgig ectotnic reestiisc toemp:eo ssoenso­
servee irt ie ordeemliml aat emasteiis clua oo,g gedtist tou d(iuomn o n­
dod io ggetti naosnet sriasAtt qteui?e) s itnot erersosmapnitceèad peo­
dicaitCloA Pr..L' antolèoq guierala mdoe lflial odseodfiicaaa r tios pon­
derael dloam an"dcah ceo seas istoev?v"ea,rs ot ipullera ergeop leler a
compiladziui noc naet aluongiov ernseCalAl Pec.;io ccuperqeumion di
I
di queasnttioolnoigv iicschtheole, a n ostdroam angduai sdaar "àin u­
mereis istono?".
Daldloam ancdiar lc'ae sisdteneiun mzeasr ipi a sasbab astnaan­za
turalmneenCltA eP2,,.a q uelcliarl cala o rnoa tuore as senczhtaei: p doi
cosseo nion ume(reai l ternet miattàe matiScohneo) ?o gagsettrstaiit ti,
dicsep esmsaoq ,u aclair atteristicuhneo gdgiesattstitonr dgaaut otnoo
unoc oncrNeetdloo ?m andcaorscsaii ainn ou mefrair edmeol mleat afi­
sicaal,m esneso ai d otltada e finidzimi eotnaef ciosmilec' ai ndvaogli­ne
taa s tabi"lcihcreoe s q'uèe lclhoce ' è".
Una lttriopd oip roblheama c ih fea rceo nl ac onoscenza matema­
ticDaau. n l atsoe mbpriafù a cdiulbei tdaenrieo ssternics hide e lcloe­
noscenze matematichsee s atceqsusiismiot eso:o s gecan ina cnhdeo ,
trovasnseimlmo nod doMi atrdiuxe, dpuiefù a repbubre seqmuparte­
treoi ,nq uessteon isr oi sumlattaetmia steimcbir easnsoec reerD t'ia.l -
9
INTROZDI ONAEL LFAI LOSODFEILAL MAA TEMATICA
trcoa ntèod ,i fficcaipliecr oem seis iapnoot uottet enqeureesc toen o­
scenNz eo.s onl golo ig gemtattie maatd iicffie,r ednegziaa t ntoins, i
possonnévo e denréet ,o cc(aqruee vsatloae n chpee ern titteào riche
delflias ciocmage l eil ett,rm oan,aid )ifferednezgeall ie ttnroonèn i,
nemmepnoos sicboinlset aatlacrutenr aa cdceillalo eri on teraczoino ne
imlo ndfoi sicloec. o ssSete a ncnoosc ìo,m fea cciaas maop eirnce h e
modos onfoa tCtoim?ef acciianmnoa nziast auptetcrohe ee s istIoln o?
problveimeapn oes atlovl oel ctoem uen d ilemsmela am:a temattrtia­c a
tad io ggeatsttir aaltltloiacr, oa n oscenza msaetmebdmriaavt einctaa re
unm istemras oel; am atemantointc raa dtiot gag eatsttir aaltltloio'r,g a ­
getdtios tuddieolm laat emasteimcbadr iav enutnam ries teqruoa:l e
scegltirqeaur ees dtuees g radeavlotleir n1aIf t iilvoes?o fi chiamano epi­
stemologiad elln'loeazs iaodmniece o noscepnezcrau p,ir obldeim i
quesgteon evreen godneof initi "epiLsalt oermaoon laolagicis­cii," .
compagndaaut nae samdeet ie ntadtiri ivsio lcvoesrtliit,iucl iu socree
deClAP .3 ·
Unf enomeno sorsportegtnloodi ce cndhtitie u tètl ios traordinario
succedseslol 'appldiicc oanzoisocneen ze maatlelsmota utddiiecolh e
mondfoi siqcuoe:llc oh Wei gncehri a«mlò' irrageifofniecdvaeocllliaea
matematAilclvaeo» l.qt uee sètv oi sctoom le' ennepsuizmzdola re i sol­
vereel ad omanddiav e"nctoam èep ossibAilltevr?oe"l .itfl ee nomeno
dell'appldieclmalabati elmiatètài i ncvaec ciet actoomu en a rgomento
pesro stecnhegerl oeig gemtattie maetsiicsitr oenaol meEnstsee.nu dno
temcal asssienc eto o,r naep raàr lsapreesn seol cdoervlso ol uimnep, a r­
ticoilnra irfee riamite ennttoad tifi ovrim ullaerp er incipali teorie scien­
tifiecshies tseennftzaiar r ei feriamdeo ngtgoea tsttir atti.
Ill ibirnot epnrdees enltosa traedt eol rliac eirmcpae gnaadat fa­
fronttaaprlreio blNeomniè .,q uinudnisa,t odreillafa il osdoefillama a ­
tematein ceam menuon ar icostrcuozmipolndeeetd lai batctointtoe m­
poranmeaou ,n 'introadluplzreio osnpee otgtgpiiiv dùei scussutsiee m i
clasdsifi iclio dseolfimlaaa t emaQtuiecsast.po i eagdea s,e mplioso c,a r­
sor ilideavtaooll vea rfioer mdeic ostruttliapv iieùss mtoed:si af efsia­
losodfiqi uceas ctoan cezèiq ouneelf loar ndiatlla' odpieD ruam mett, di­
scuspsrao pirnai poe rteur reasu,tn aa p promcicnioor iPteairrrl ie os.t o,
iclo struttsiièrv iivsemilona tteor essadnaut nip susnitdmoivo i smtaa­
tematmiach oaa, t tiproactloo' attednezfiii olnoeIs nouftidi.il reql uoe,­
stnoo nèu nd ifeftotroas,ne zu inp regmiaon ,es pielg'ae sclduasli one
volume.
I.n dileimnqm uae sètc ioonnoesi cnli eutttoes roatinttlouo mr deai" idlemdim a
Benac,ce frrr.a fB"(e1n39a)7c.e rraf
IO
PREMESSA
Infiunnepa,i ccnooltmaae todolloamg aitceam:a dtais ceam,p hrae ,
attilr'aattot ednezfiiil oonsceoo fmiue n r ompicdaarp ios olQvueerset.a
metafaonrdar epbrbeess uasl e rpiroo,p preidroa riegl i uspteosa ol le
varfiileo sdoeflimleaa t emaqtuiecsaut;le t iamned rebvbiescrtooem vea ­
rite ntadtiri ivsio livpleu rzeze ln eo na ndrebmbaepirr oe tsreo pspuol
serLiaos .t oriinaf,ac tiht adi a,ta ol meunnola e zisotinr ea:dt iut nap uzz­
led iffiLcemi ilgel.it oersdite erl e amveis is ondoe diccaotnae c cani­
mentsoe,n gziau ngaedur nesa o luzuinoinvee rsaclomnednitTvelIi esta­.
toroes seqruviinl demi o ssfei naodo rtae ntpaetrrei solqvueerscetu o­
bod iR ubicko ncetets ueaa llfleia;nd ee llleat tsuernat iidlse ssei ddeir io
giocdaars coilq ou,e sltiob arvor ebbe riaslgu gsoic uonptoo.
Ringraznitaim e
Pardtemela terqiupairl ees eènr tiaptrdoea slmoli taae dsidi o tto(rPalteob ani,
201,0s ecoent deorc zaopl i)otH.oo q uiunndd io ppdieob nietio confronti di
LuiPgeir issedi iPn aosttqFour aalsec cohmleil h aa,n sneog uiinet not rai mbi
lavnoermlii gldieomiro edp io ssibili.
Ung rapzairet iacncoehl Paair eer dGainaireeelF tert aan cBeoscccacu hnei ,
hanlneoti vtloo l unmeels luiaan teerf eozrznpair teoz iocsoimsmseiAnmlti­i .
tretuttainltiso t siaso tunigo g erdiiVm ietnttMoior riaoMt aor,Pc aon ez aA n­
dreSae rieF.nr ancBeesrcètro oe spboinilsnead idreellte tgogt eorcmoce io­
nonghpiraensone enllti ebs ruqolu, a hlafe o rnuittiol iisnsdiimcea zioni.
Sonmoo lto agdEr nartiMoca or tpienarov erdmaitl op' poortduidn ii­tà
scutceolrnue i v adrqiiu ee sdtiifli oonisidao e flmlaat emaitmipcaars,ae nmd­o
prtea ntissimo.
Avera vultpaoo ssidbici olliltaàcb ooInrv aaKrnae s eca o nfrontarmi con
lusiue llq uestdienole noi- logeid ceiloslbmeio e ezpiiosnit emalo plloagtioc­he
nismmaot emmaith iaac iou taca htioa lrieied resm uqi u etsetmii . aGnrcahzei e
adA ndérF uhmran aeim embrdies lme inairod iL ogiesc eam andteilclaa
GoetUhnei vedriFs riatnacto forte.
GrazaMi aes simCialriraManarota tF,ea ov aCraemttpio samep Viaie tr­o
torMioor adteoDl,i partdiiFm ielnotdsoiPo afdioapv eaar,v feorr nuinat m­o
bieindteea llesa t peesdruev rloa l ume.
GrazaGi iea nlMuorcpiae a rv ecerrud tnoe plr ogee tBata or bCaarnae ­
streeR lolbieG ritaan pneiirnpl ir eziosspuipsosreitdmoio t oriale.
Grazaineca hM ea riLnaat eera zlsa us ot fad felPlrao gpeedric tul rraae ­
dazionale.
Inifnger,a azmii ieea im actoii nqeu iMala irBniaiae tlzai nplgro:er soe nza
ès tautnfaao ndtige i odiuar alnast tee sduiqr uae stoe i lnmi oblartloimt, or ­i
menti.
II