{"id":5380,"date":"2010-09-18T15:17:48","date_gmt":"2010-09-18T13:17:48","guid":{"rendered":"http:\/\/egophobia.ro\/?p=5380"},"modified":"2011-02-05T21:35:32","modified_gmt":"2011-02-05T19:35:32","slug":"se-poate-sus%c8%9bine-conven%c8%9bionalismul-radical-in-filosofia-matematicii-i","status":"publish","type":"post","link":"https:\/\/egophobia.ro\/?p=5380","title":{"rendered":"Se poate sus\u021bine conven\u021bionalismul radical \u00een filosofia matematicii? [I]"},"content":{"rendered":"

[continuarea studiului Despre adev\u0103rul propozi\u0163iilor matematicii \u015fi logicii la L. Wittgenstein<\/em>]<\/strong><\/p>\n

de Cristina Nemerovschi<\/p>\n

\nM. Dummett, \u00een articolul Wittgenstein\u2019s Philosophy of Mathematics<\/em>, face distinc\u021bie \u00eentre un \u201cconven\u021bionalism modificat\u201d, care presupune c\u0103 adev\u0103rul necesar deriv\u0103 din conven\u021bii lingvistice, dar nu deriv\u0103 direct ci este o consecin\u021b\u0103 a acestor conven\u021bii, \u0219i un alt tip de conven\u021bionalism \u2013 cel al lui Wittgenstein \u2013 un conven\u021bionalism strict care consider\u0103 c\u0103 necesitatea logic\u0103 \u0219i matematic\u0103 \u201ceste \u00eentotdeauna exprimarea direct\u0103 a unei conven\u021bii lingvistice\u201d.<\/p>\n

\nPrimul tip de conven\u021bionalism este cel pe care \u00eel \u00eent\u00e2lnim la empirismul logic, spune Dummett. Acest fel de conven\u021bionalism, numit \u0219i moderat deoarece nu presupune o derivare direct\u0103 a adev\u0103rului logic din conven\u021bii, s-a dovedit inconsistent. \u00cen plus, cel practicat de empiri\u0219tii logici \u2013 conven\u021bionalism moderat, \u00een opinia lui Dummett \u2013 se consider\u0103 dep\u0103\u0219it odat\u0103 cu apari\u021bia articolului lui Quine, Dou\u0103 dogme ale empirismului<\/em>. Articolul lui Quine a impus concluzia c\u0103 nu putem distinge at\u00e2t de radical, precum o f\u0103ceau reprezentan\u021bii pozitivismului logic, \u00eentre adev\u0103ruri analitice \u0219i adev\u0103ruri sintetice, deci nu putem sus\u021bine c\u0103 un adev\u0103r al logicii sau al matematicii este necesar doar \u00een virtutea unor conven\u021bii lingvistice. <\/p>\n

\nBaker \u0219i Hacker apreciaz\u0103 c\u0103 se pot formula dou\u0103 argumente consistente \u00eempotriva conven\u021bionalismului moderat (cei doi autori p\u0103streaz\u0103 denumirea dat\u0103 de Dummett conven\u021bionalismului logic-empirist):<\/p>\n

\n(1)\tDefini\u021biile sunt reguli de substituire a expresiilor<\/strong><\/p>\n

\nDemonstra\u021bia faptului c\u0103 o propozi\u021bie este analitic\u0103 trebuie s\u0103 porneasc\u0103 de la o instan\u021b\u0103 a unei propozi\u021bii a logicii (cei doi autori nu argumenteaz\u0103 cu acurate\u021be aceast\u0103 premis\u0103). \u00cen consecin\u021b\u0103, izolarea adev\u0103rurilor logice este presupus\u0103 \u00een defini\u021bia adev\u0103rului analitic \u0219i de formularea conven\u021biilor lingvistice; astfel, adev\u0103rurile logice nu sunt produsul exclusiv al conven\u021biei.<\/p>\n

\nAcest argument nu este \u00eens\u0103 formulat cu prea mult\u0103 claritate \u2013 autorii vor probabil s\u0103 sus\u021bin\u0103 c\u0103 o teorie ce pune conven\u021biile la baza necesit\u0103\u021bii nu poate evita un cerc vicios. El se formeaz\u0103 ca urmare a \u00eencerc\u0103rii de a explica necesitatea prin conven\u021bii, care la r\u00e2ndul lor nu pot fi explicate dec\u00e2t tot prin necesitate conven\u021bional\u0103. Dac\u0103 se \u00eencearc\u0103 evitarea acestui cerc vicios, trebuie s\u0103 se recurg\u0103 \u0219i la alt\u0103 no\u021biune \u00een afara celei de \u201enecesitate lingvistic\u0103\u201d.<\/p>\n

\n(2)\tAdev\u0103rurile necesare (fie \u0219i numai ale logicii) nu pot fi epuizate exhaustiv prin enumerare<\/strong><\/p>\n

\nAstfel, dac\u0103 sunt adev\u0103rate \u00een virtutea conven\u021biilor, trebuie s\u0103 mai existe ceva (\u00een metalimbaj) cum ar fi, de pild\u0103, principiul instan\u021bierii universale care este indispensabil pentru specificarea consecin\u021belor conven\u021biilor. Dar pentru c\u0103 aceste principii logice stau \u00een afara conven\u021biilor \u2013 \u00een metalimbaj \u2013 no\u021biunea de adev\u0103r prin conven\u021bie aduce o simplificare mai pu\u021bin esen\u021bial\u0103 pentru filosofie dec\u00e2t p\u0103rea s\u0103 promit\u0103, concluzioneaz\u0103 Baker \u0219i Hacker \u00een Wittgenstein. Rules, Grammar and Necessity.<\/em><\/p>\n

\nPotrivit celor doi autori, conven\u021bionalismul standard, cel moderat, are o lacun\u0103: enumerarea adev\u0103rurilor necesare \u00een limbajul obiect ca adev\u0103ruri prin conven\u021bie presupune alte adev\u0103ruri necesare \u00een metalimbaj, a c\u0103ror necesitate r\u0103m\u00e2ne neelucidat\u0103.<\/p>\n

\nConven\u021bionalismul standard este superficial, deoarece \u201caccept\u00e2nd c\u0103 enun\u021burile necesare nu sunt \u00eenregistr\u0103ri directe ale conven\u021biilor, ci mai degrab\u0103 \u00eentr-o m\u0103sur\u0103 mai mic\u0103 sau mai mare consecin\u021be ale conven\u021biilor, r\u0103m\u00e2ne neexplicat statutul aser\u021biunii c\u0103, dac\u0103 adopt\u0103m anumite conven\u021bii ca axiome \u00eempreun\u0103 cu altele considerate ca principii de inferen\u021b\u0103, atunci suntem obliga\u021bi s\u0103 ader\u0103m la conven\u021bia con\u021binut\u0103 \u00een teorem\u0103\u201d, spun Baker \u0219i Hacker.<\/p>\n

\nPozi\u021bia lui Dummett sub acest aspect este aproape identic\u0103 \u2013 conven\u021bionalistul moderat, \u00eentrebat care este statutul principiilor logice \u00een acord cu care trecem la de la axiome la teoreme, va r\u0103spunde c\u0103 \u201csubscrierea la aceste principii este la r\u00e2ndul ei expresia adopt\u0103rii unor conven\u021bii lingvistice\u201d. Aceast\u0103 pozi\u021bie este superficial\u0103, consider\u0103 Dummett, \u00eentruc\u00e2t nu d\u0103 seama despre semnifica\u021bia pe care o are expresia c\u0103 o conven\u021bie are anumite consecin\u021be, expresie care ar fi esen\u021bial\u0103 pentru conven\u021bionalism \u0219i care, dac\u0103 ar primi o explicitare satisf\u0103c\u0103toare, ar putea s\u0103 eviden\u021bieze anumite avantaje pe care le are conven\u021bionalismul \u00een raport cu alte pozi\u021bii din filosofia matematicii. <\/p>\n

\nConcluzia argumentului (2), formulat de Baker \u0219i Hacker, ar fi aceea c\u0103 sursa adev\u0103rului necesar nu poate fi explicat\u0103 prin conven\u021bii.<\/p>\n

\nCriticile de mai sus sunt valabile, \u00een accep\u021bia celor care le formuleaz\u0103, pentru conven\u021bionalismul sus\u021binut de empirismul logic. Sunt ele \u00eens\u0103 valabile \u0219i pentru conven\u021bionalismul wittgensteinian? R\u0103m\u00e2ne s\u0103 analiz\u0103m acest aspect \u00een capitolul urm\u0103tor<\/a>.<\/p>\n

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

\nBaker & Hacker, Wittgenstein. Rules, Grammar and Necessity, Basil Blackwell, Oxford, 1985
\nDeloche C., La Philosophie Des Mathematiques chez Wittgenstein, CNRS Editions, Paris, 1995
\nDummett M, Wittgenstein\u2019s Philosophy Of Mathematics, Harvard University Press, 1978
\nHempel C, On The Nature Of Mathematical Truth, American Philosophical Review, nr. 25, 1945
\n\u0162urlea M., Filosofia Matematicii, Ed. Univ. Bucure\u015fti, Bucure\u015fti, 2002
\nWittgenstein L., Caietul albastru, Ed. Humanitas, Bucure\u015fti, 1993
\nWittgenstein L., Remarks on the Foundations of Mathematics, Penguin Books, Londra, 1965
\nWittgenstein L., Tractatus Logico-Philosophicus, Ed. Humanitas, Bucure\u015fti, 2001<\/p>\n","protected":false},"excerpt":{"rendered":"

[continuarea studiului Despre adev\u0103rul propozi\u0163iilor matematicii \u015fi logicii la L. Wittgenstein] de Cristina Nemerovschi M. Dummett, \u00een articolul Wittgenstein\u2019s Philosophy of Mathematics, face distinc\u021bie \u00eentre un \u201cconven\u021bionalism modificat\u201d, care presupune c\u0103 adev\u0103rul necesar deriv\u0103 din conven\u021bii lingvistice, dar nu deriv\u0103 direct ci este o consecin\u021b\u0103 a acestor conven\u021bii, \u0219i un alt tip de conven\u021bionalism \u2013 […]<\/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":[615,27],"tags":[516,1150,1117,32],"class_list":["post-5380","post","type-post","status-publish","format-standard","hentry","category-egophobia-28","category-filosofie","tag-cristina-nemerovschi","tag-egophobia-28","tag-filosofie","tag-morgothya"],"jetpack_featured_media_url":"","jetpack_sharing_enabled":true,"jetpack_shortlink":"https:\/\/wp.me\/p6DakB-1oM","_links":{"self":[{"href":"https:\/\/egophobia.ro\/index.php?rest_route=\/wp\/v2\/posts\/5380","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=5380"}],"version-history":[{"count":7,"href":"https:\/\/egophobia.ro\/index.php?rest_route=\/wp\/v2\/posts\/5380\/revisions"}],"predecessor-version":[{"id":6629,"href":"https:\/\/egophobia.ro\/index.php?rest_route=\/wp\/v2\/posts\/5380\/revisions\/6629"}],"wp:attachment":[{"href":"https:\/\/egophobia.ro\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=5380"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/egophobia.ro\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=5380"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/egophobia.ro\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=5380"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}