20. y\u00fczy\u0131l matematiksel mant\u0131k tarihinin en \u00f6nemli olay\u0131 Kurt G\u00f6del\u2019in matemati\u011fin temelleri hakk\u0131nda kan\u0131tlad\u0131\u011f\u0131 teoremlerdir. Kesinlik, tutarl\u0131l\u0131k, taml\u0131k gibi niteliklerin matemati\u011fe y\u00fcklenmesinin en \u00f6nemli nedeni, matemati\u011fin aksiyomlardan t\u00fcretilen \u201cdo\u011fru\u201d \u00f6nermelerinin, yani teoremlerin kesin olarak kan\u0131tlanabilir olmas\u0131yd\u0131. B\u00f6ylece \u201cdo\u011fruluk\u201d ve kan\u0131tlanabilirlik \u00f6rt\u00fc\u015ft\u00fcr\u00fcl\u00fcyordu. Matemati\u011fin teoremlerinin do\u011fru iseler do\u011fruluklar\u0131 kesinlikle kan\u0131tlanabilen, do\u011fru de\u011filseler yine do\u011fru olmad\u0131klar\u0131 kesin olarak kan\u0131tlanabilen \u00f6nermeler olduklar\u0131, dolay\u0131s\u0131yla matematikte kesinlik ve tutarl\u0131l\u0131\u011f\u0131n tam olarak egemen oldu\u011fu kabul edilmi\u015fti. G\u00f6del bu kabullerin ve beklentilerin san\u0131ld\u0131\u011f\u0131 gibi sa\u011flam olmad\u0131\u011f\u0131n\u0131 yine matematikten yola \u00e7\u0131karak kesin olarak kan\u0131tlam\u0131\u015ft\u0131r. Whitehead ve Russell\u2019\u0131n matemati\u011fin mant\u0131ksal temelleri konusundaki an\u0131tsal \u00e7al\u0131\u015fmas\u0131 olan Principia Mathematica\u2019y\u0131 ele alarak, temellerin hep eksik kalaca\u011f\u0131n\u0131 g\u00f6stermi\u015ftir. G\u00f6del, do\u011fal say\u0131lar aritmeti\u011fini kapsayan bir bi\u00e7imsel dizgede, karar verilemeyen \u00f6nermeler oldu\u011funu kan\u0131tlam\u0131\u015ft\u0131r; yani bu \u00f6nermeler ne kan\u0131tlanabilirler ne de bunlar\u0131n bi\u00e7imsel de\u011fillemeleri kan\u0131tlanabilir. Ama \u00f6te yandan, bu karar verilemeyen \u00f6nermelerin do\u011fru olduklar\u0131 \u00fcst-matematiksel ak\u0131l y\u00fcr\u00fctmelerle g\u00f6sterilebilir. Ayr\u0131ca G\u00f6del, do\u011fal say\u0131lar aritmeti\u011fini kapsayan bir bi\u00e7imsel dizgenin tutarl\u0131l\u0131\u011f\u0131n\u0131n, bu dizgenin i\u00e7inde kan\u0131tlanamayaca\u011f\u0131n\u0131 da kan\u0131tlam\u0131\u015ft\u0131r. G\u00f6del\u2019in \u00e7al\u0131\u015fmalar\u0131n\u0131n sonu\u00e7lar\u0131 matemati\u011fin kendi i\u00e7sel s\u0131n\u0131rl\u0131l\u0131klar\u0131 oldu\u011funu ortaya koymu\u015ftur. \u201cHi\u00e7 ku\u015fku yok ki, benim ortaya \u00e7\u0131kard\u0131\u011f\u0131m \u00e7al\u0131\u015fma bir yan\u0131yla, Nagel ve Newman\u2019\u0131n kitab\u0131ndan kaynaklanm\u0131\u015ft\u0131r.\u201d \u2013Douglas R. Hofstadter, G\u00f6del, Escher, Bach\u2019\u0131n yazar\u0131 \u2018G\u00f6del\u2019in kan\u0131tlamas\u0131 \u00fczerine yaz\u0131lm\u0131\u015f en iyi kitap.\u201d \u2013Scientific American \u201cOla\u011fan\u00fcst\u00fc bir yorumlama.\u201d \u2013Nature K <\/p>\n","protected":false},"excerpt":{"rendered":"
20. y\u00fczy\u0131l matematiksel mant\u0131k tarihinin en \u00f6nemli olay\u0131 Kurt G\u00f6del\u2019in matemati\u011fin temelleri hakk\u0131nda kan\u0131tlad\u0131\u011f\u0131 teoremlerdir. Kesinlik, tutarl\u0131l\u0131k, taml\u0131k gibi niteliklerin matemati\u011fe y\u00fcklenmesinin en \u00f6nemli nedeni, matemati\u011fin [\u2026]<\/span><\/p>\n","protected":false},"featured_media":0,"template":"","meta":{"_monsterinsights_skip_tracking":false,"_monsterinsights_sitenote_active":false,"_monsterinsights_sitenote_note":"","_monsterinsights_sitenote_category":0},"product_brand":[],"product_cat":[13005,16724],"product_tag":[],"class_list":{"0":"post-782420","1":"product","2":"type-product","3":"status-publish","5":"product_cat-bilim-muhendislik","6":"product_cat-matematik","7":"pa_cilt-ciltsiz","8":"pa_tur-kitap","9":"pa_yayinevi-alfa-yayinlari","10":"pa_yazar-ernest-nagel-james-r-newman","12":"first","13":"instock","14":"sale","15":"shipping-taxable","16":"purchasable","17":"product-type-simple"},"_links":{"self":[{"href":"https:\/\/roveyayinevi.com.tr\/index.php\/wp-json\/wp\/v2\/product\/782420","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/roveyayinevi.com.tr\/index.php\/wp-json\/wp\/v2\/product"}],"about":[{"href":"https:\/\/roveyayinevi.com.tr\/index.php\/wp-json\/wp\/v2\/types\/product"}],"wp:attachment":[{"href":"https:\/\/roveyayinevi.com.tr\/index.php\/wp-json\/wp\/v2\/media?parent=782420"}],"wp:term":[{"taxonomy":"product_brand","embeddable":true,"href":"https:\/\/roveyayinevi.com.tr\/index.php\/wp-json\/wp\/v2\/product_brand?post=782420"},{"taxonomy":"product_cat","embeddable":true,"href":"https:\/\/roveyayinevi.com.tr\/index.php\/wp-json\/wp\/v2\/product_cat?post=782420"},{"taxonomy":"product_tag","embeddable":true,"href":"https:\/\/roveyayinevi.com.tr\/index.php\/wp-json\/wp\/v2\/product_tag?post=782420"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}