{"id":4041,"date":"2010-03-20T22:49:37","date_gmt":"2010-03-20T20:49:37","guid":{"rendered":"http:\/\/egophobia.ro\/?p=4041"},"modified":"2010-03-20T22:49:37","modified_gmt":"2010-03-20T20:49:37","slug":"1-cantor-aristotel-dialehteismul-%e2%80%93-azi-cantor","status":"publish","type":"post","link":"https:\/\/egophobia.ro\/?p=4041","title":{"rendered":"(1) Cantor, Aristotel, Dialehteismul \u2013 Azi, Cantor"},"content":{"rendered":"

(postmodernitate versus postmodernism [XXI])<\/font><\/p>\n

de Gorun Manolescu<\/p>\n

\n1. <\/strong><\/p>\n

\nDou\u0103 mul\u021bimi. Una a cailor, alta a c\u0103l\u0103re\u021bilor. Dac\u0103 se \u00eemperecheaz\u0103 fiecare cal cu un c\u0103l\u0103re\u021b, este posibil ca: ori unul sau mai mul\u021bi cai s\u0103 r\u0103m\u00e2n\u0103 f\u0103r\u0103 c\u0103l\u0103re\u021bi; ori invers; ori s\u0103 existe numai perechi. \u00cen ultimul caz, cele dou\u0103 mul\u021bimi se zice c\u0103 sunt echipotente. De aici \u00abputerea\u00bb unei mul\u021bimi sau \u00abcardinalul\u00bb acesteia. Adic\u0103, num\u0103rul de elemente ale unei mul\u021bimi.\u201d<\/p>\n

2.<\/strong><\/p>\n

\nTot de aici pleac\u0103 Cantor: ia un \u0219ir de numere \u00eentregi, ordonate cresc\u0103tor. \u0218i ia alt \u0219ir asemenea, dar cu primul element imediat superior celui mai mare din \u0219irul precedent. Ambele av\u00e2nd acela\u0219i num\u0103r de elemente (mul\u021bimi \u00abechipotente\u00bb). \u0218i le \u00eemperecheaz\u0103. \u0218i mai observ\u0103 c\u0103 lucrul acesta poate s\u0103-l fac\u0103 ori de c\u00e2te ori are chef. P\u00e2n\u0103 la infinit. Deoarece \u0219irul numerelor naturale se \u00eentinde la infinit. \u0218i uite a\u0219a apar mul\u021bimile infinit num\u0103rabile. \u0218i primul num\u0103r transfinit: cardinalul unei astfel de mul\u021bimi.<\/p>\n

Cantor noteaz\u0103 [1]<\/a>: \u201e[P\u00e2n\u0103 acum a func\u021bionat, \u0219i func\u021bioneaz\u0103, din p\u0103cate] un anumit principiu recomandat tuturor [cel al finalit\u0103\u021bii]\u2026.chiar dac\u0103 este oarecum simplu \u0219i banal; el trebuie s\u0103 [se] foloseasc\u0103 pentru ca pl\u0103cerea \u00eenaripat\u0103 de specula\u021bia \u0219i de concep\u021bia matematic\u0103\u201d \u2026.s\u0103 nu o ia razna \u0219i s\u0103 cad\u0103 \u00een \u201epericolul de a ajunge \u00een pr\u0103pastia \u00abtranscendentului\u00bb, acolo unde, spre \u00eenfrico\u0219are \u0219i groaz\u0103 salvatoare, se spune c\u0103 \u00abtotul este posibil\u00bb\u2026 Odat\u0103 stabilite aceste lucruri, cine \u0219tie dac\u0103 nu tocmai punctul de vedere al finalit\u0103\u021bii a fost singurul care a determinat pe autorii opiniei ca tuturor for\u021belor pline de n\u0103zuin\u021be, care ajung a\u0219a de u\u0219or \u00een pericol prin arogan\u021b\u0103 \u0219i lips\u0103 de modera\u021bie, s\u0103 le fie recomandat\u0103 finalitatea\u2026 de\u0219i \u00een ea nu se poate g\u0103si un principiu fecund\u201d. \u0218i, mai departe: \u201deste surprinz\u0103tor c\u0103 p\u00e2n\u0103 acum a lipsit cineva care, dup\u0103 \u0219tiin\u021ba mea, s\u0103 fi \u00eentreprins o formulare mai complet\u0103 \u0219i mai bine dec\u00e2t am \u00eencercat eu aici\u201d\u2026.\u0219i \u2026\u201emai cred c\u0103 se pot admite num\u0103r\u0103ri \u2026 nu numai la mul\u021bimile finite, dar \u0219i la cele infinite\u201d. Lucru pe care \u00eel face prin introducerea cardinalului unei mul\u021bimi num\u0103rabile (ca prim num\u0103r transfinit).<\/p>\n

3.<\/strong><\/p>\n

\nDac\u0103 s-ar fi oprit aici, ar fi sc\u0103pat de ce-l p\u00e2ndea. Dar nu se ast\u00e2mp\u0103r\u0103. <\/p>\n

Un prim pas spre pr\u0103pastie \u00eel face c\u00e2nd \u00eencepe s\u0103 se joace cu mai multe cardinale (numere transfinite) de mul\u021bimi infinit num\u0103rabile.<\/p>\n

Lu\u00e2nd, de exemplu, \u0219irul de numere 1, 2, 3,\u2026.,\u00ed \u0219i spun\u00e2nd c\u0103 \u00ed este limita spre care tinde \u0219irul infinit num\u0103rabil \u0219i, \u00een acela\u0219i timp, cardinalul (\u00abalephul\u00bb \u00e11 cum \u00eel nume\u0219te Cantor acest prim num\u0103r transfinit) al \u0219irului, Cantor g\u0103se\u0219te, \u00een pa\u0219ii ulteriori, c\u0103 \u201enu e nimic scandalos s\u0103 ne imagin\u0103m c\u0103 dup\u0103 acest prim \u00abaleph\u00bb \u00ed\/ \u00e11 ar putea urma un al doilea al unui \u0219ir care \u00eencepe cu \u00e11+1 \u0219i al c\u0103rui nou \u00abaleph\u00bb este \u00e11+2 \u0219.a.m.d.. <\/p>\n

\nProblema este c\u0103 pentru \u0219irul \u00e11, \u00e11+1, \u00e11+2\u2026. Nu mai exist\u0103 nici o \u00eenchidere!<\/p>\n

4.<\/strong><\/p>\n

\nAcum, Cantor este pe marginea pr\u0103pastiei. \u0218i se arunc\u0103 cu capul \u00eenainte, \u00een momentul \u00een care ajunge la infinitul continuu, adic\u0103 \u201ene-num\u0103rabil\u201d al numerelor reale. Recurg\u00e2nd \u0219i la alte considera\u021bii conexe (printre altele chiar conceptul de \u00abconexiune\u00bb) \u2013 stop c\u0103 v-am (ne-am) f\u00e3cut capul calendar.<\/p>\n

\nNu o s\u0103 v\u0103 mai pun, \u00een continuare, imagina\u021bia (matematic\u0103) la \u00eencercare. Ci o s\u0103 recurg la c\u00e2teva exemple (consecin\u021be) \u2013 zic eu, sugestive \u2013 ale \u00abalephurilor\u00bb cantoriene [2]<\/a>.<\/p>\n

\n\u201eS\u0103 ne \u00eenchipuim c\u0103 pe o foaie de h\u00e2rtie exist\u0103 dou\u0103 puncte A \u0219i B, la distan\u021b\u0103 de 1 cm unul de altul. Tras\u0103m segmentul de dreapt\u0103 care une\u0219te A cu B. C\u00e2te puncte exist\u0103 pe acest segment? Cantor demonstreaz\u0103 c\u0103 exist\u0103 mai multe dec\u00e2t un num\u0103r infinit. Pentru a umple complet segmentul, e necesar un num\u0103r mai mare dec\u00e2t infinitul: num\u0103rul \u00abtau\u00bb (\u0219i nu num\u0103rul \u00abaleph\u00bb cum gre\u0219it se spune \u00een [2]<\/a>; \u00abtau\u00bb cuprinz\u00e2nd toate \u00abaleph-urile\u00bb posibile n.m. G.M.).<\/p>\n

\nAcest num\u0103r \u00abtau\u00bb este egal cu fiecare din p\u0103r\u021bile sale. Dac\u0103 se \u00eemparte segmentul \u00een zece p\u0103r\u021bi egale, vor exista tot at\u00e2tea puncte \u00eentr-una din p\u0103r\u021bi c\u00e2te sunt pe tot segmentul. Dac\u0103, plec\u00e2nd de la segmentul \u00een cauz\u0103, se construie\u0219te un p\u0103trat, vor fi tot at\u00e2tea puncte pe segment ca \u0219i pe suprafa\u021ba p\u0103tratului. Dac\u0103 se construie\u0219te un cub, vor fi tot at\u00e2tea puncte pe segment ca \u0219i \u00een tot volumul cubului. \u0218i a\u0219a mai departe p\u00e2n\u0103 la\u2026 infinit.<\/p>\n

\n\u00cen aceast\u0103 matematic\u0103 a transfinitului, care studiaz\u0103 numerele \u00abtau\u00bb \u0219i \u00abaleph\u00bb, partea este egal\u0103 cu \u00eentregul. \u201eEste absolut demen\u021bial, dac\u0103 ne plas\u0103m \u00een punctul de vedere al ra\u021biunii clasice \u0219i totu\u0219i se poate demonstra. \u0218i iat\u0103 cum matematicile contemporane superioare se \u00eent\u00e2lnesc cu \u00abTabula Smaragdina\u00bb a lui Hermes Trimegistos (\u00abceea ce se afl\u0103 sus este aidoma cu ceea ce se afl\u0103 jos\u00bb) \u0219i cu intui\u021bia unor poe\u021bi ca William Blake (\u00ab\u00eentreg universul \u00eentr-un fir de nisip\u00bb).\u201d Ca s\u0103 nu mai vorbesc de unele texte ale lui Borges sau de holografie \u0219i \u00abholomi\u0219carea\u00bb lui David Bohm [3]<\/a>, sau de Philon din Alexandria (primul teolog cre\u0219tin): \u201esubstan\u021ba lui Dumnezeu se revars\u0103 indefinit f\u0103r\u0103 pierdere\u201d [4]<\/a>.<\/p>\n

5.<\/strong><\/p>\n

\nRezultatele lui Cantor sunt \u00eenc\u0103 discutate de matematicieni. Dintre care unii spun c\u0103 sunt de nesus\u021binut din punct de vedere \u00ablogic\u00bb (evident, este vorba de logica clasic\u0103 aristotelic\u0103). La care partizanii Transfinitului exclam\u0103: \u00abNimeni nu ne va alunga din Paradisul cantorian!\u00bb.<\/p>\n

\nCantor a spus c\u0103 toate descoperirile lui i-au fost revelate de Dumnezeu. Dar Dumnezeu nu este infinitul, ci Absolutul. \u0218i a \u00eennebunit. Lucru pe care l-am putea face \u0219i noi. Dac\u0103 nu ne vom p\u0103stra cump\u0103tul pentru ceea ce urmeaz\u0103 data viitoare. (Adic\u0103 Aristotel).<\/p>\n

\nNote:<\/strong><\/p>\n

<\/a> [1]. citat \u00een: Oskar Becker, \u201eFundamentele Matematicii\u201d , Ed. \u0218tiin\u021bific\u0103, 1968
\n<\/a>[2]. Louis Pauvels et Jaques Bergier, \u201e Le matin des magiciens\u201d, Galimard, 1960
\n<\/a>[3]. David Bohm, \u201ePlenitudinea lumii \u0219i ordinea ei\u201d, Humanitas, 1980
\n<\/a>[4]. Philon din Amexandria, \u201eComentariu alegoric al legilor sfinte dup\u0103 lucrarea de \u0219ase zile\u201d, Herald, 2006 <\/p>\n","protected":false},"excerpt":{"rendered":"

(postmodernitate versus postmodernism [XXI]) de Gorun Manolescu 1. Dou\u0103 mul\u021bimi. Una a cailor, alta a c\u0103l\u0103re\u021bilor. Dac\u0103 se \u00eemperecheaz\u0103 fiecare cal cu un c\u0103l\u0103re\u021b, este posibil ca: ori unul sau mai mul\u021bi cai s\u0103 r\u0103m\u00e2n\u0103 f\u0103r\u0103 c\u0103l\u0103re\u021bi; ori invers; ori s\u0103 existe numai perechi. \u00cen ultimul caz, cele dou\u0103 mul\u021bimi se zice c\u0103 sunt echipotente. […]<\/p>\n","protected":false},"author":5,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"jetpack_post_was_ever_published":false,"_jetpack_newsletter_access":"","_jetpack_dont_email_post_to_subs":false,"_jetpack_newsletter_tier_id":0,"_jetpack_memberships_contains_paywalled_content":false,"_jetpack_memberships_contains_paid_content":false,"footnotes":""},"categories":[507,27,51],"tags":[1147,1117,28,52],"class_list":["post-4041","post","type-post","status-publish","format-standard","hentry","category-egophobia-26","category-filosofie","category-postmodernitate-vs-postmodernism","tag-egophobia-26","tag-filosofie","tag-gorun-manolescu","tag-postmodernitate-versus-postmodernism"],"jetpack_featured_media_url":"","jetpack_sharing_enabled":true,"jetpack_shortlink":"https:\/\/wp.me\/p6DakB-13b","_links":{"self":[{"href":"https:\/\/egophobia.ro\/index.php?rest_route=\/wp\/v2\/posts\/4041","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/egophobia.ro\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/egophobia.ro\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/egophobia.ro\/index.php?rest_route=\/wp\/v2\/users\/5"}],"replies":[{"embeddable":true,"href":"https:\/\/egophobia.ro\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=4041"}],"version-history":[{"count":2,"href":"https:\/\/egophobia.ro\/index.php?rest_route=\/wp\/v2\/posts\/4041\/revisions"}],"predecessor-version":[{"id":4043,"href":"https:\/\/egophobia.ro\/index.php?rest_route=\/wp\/v2\/posts\/4041\/revisions\/4043"}],"wp:attachment":[{"href":"https:\/\/egophobia.ro\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=4041"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/egophobia.ro\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=4041"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/egophobia.ro\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=4041"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}