\u00d6n not: Konunun ilgilisi hayli uzun bir kaynak\u00e7a listesine sahiptir elbet. Yeni ilgilenebilecek okuyucu ise, \u015fu iki toplu kaynaktan se\u00e7im yapabilir. (*)<\/p>\n
\u00d6nceki pek \u00e7ok yaz\u0131m\u0131zda \u00e7e\u015fitli s\u00f6z\u00fcm ona paradokslara de\u011finmi\u015f idik. \u00d6rne\u011fin Zeno Paradokslar\u0131\u2019nda, g\u00f6r\u00fcn\u00fc\u015fteki zorlu\u011fun tamamen s\u00f6zc\u00fcklerden kaynakland\u0131\u011f\u0131n\u0131 de\u011ferlendirmi\u015ftik. \u0130kinci \u00f6rnek olarak de\u011ferlendirdi\u011fimiz Hilbert\u2019in Sonsuz Oteli (**) konusu hakk\u0131nda da pek \u00e7ok hem de pek e\u011flenceli kaynak mevcuttur. Asla yap\u0131lamayacak olan, yap\u0131lmas\u0131n\u0131n m\u00fcmk\u00fcn olmad\u0131\u011f\u0131 bir s\u00f6z\u00fcm ona sonsuz odal\u0131 otel hakk\u0131nda ahk\u00e2m kesmenin tad\u0131na doyulabilir mi?<\/p>\n
Ba\u015fka herhangi bir ki\u015finin \u00fcst\u00fcnde durdu\u011funa \u015fahit olmad\u0131\u011f\u0131m bir soruya burada yer vereyim. Oda say\u0131s\u0131 s\u0131n\u0131rl\u0131, yani oda say\u0131s\u0131 (diyelim ki, 100\u2019den veya 1000\u2019den yahut 10000\u2019den) herhangi bir Tam Say\u0131\u2019dan k\u00fc\u00e7\u00fck ama alan\u0131 sonsuz olan hayali bir otele gelen misafir say\u0131s\u0131 bilinen her Tam Say\u0131\u2019dan b\u00fcy\u00fck (yani, yayg\u0131nca kullan\u0131lan s\u00f6zc\u00fckle \u2018sonsuz\u2019) olsayd\u0131 ne yapmak gerekirdi; t\u00fcm misafirlerin o otel odalar\u0131nda konaklamas\u0131n\u0131 sa\u011flamak i\u00e7in?<\/p>\n
Biraz daha a\u00e7al\u0131m.
\nDiyelim ki, 10000 odal\u0131 b\u00f6yle bir otelde 100 misafir konaklamakta. Ertesi g\u00fcn 1000 misafir daha geldi. Ama, bir sonraki g\u00fcnde \u2018sonsuz\u2019 misafir geldi. (Sonsuz say\u0131 de\u011fildir. Bu nedenle de \u015fu ifade yanl\u0131\u015ft\u0131r, anlams\u0131zd\u0131r: \u201cAma, bir sonraki g\u00fcnde \u2018sonsuz\u2019 say\u0131da misafir geldi.\u201d)
\nBu son gelen misafirlerin bu otelde konaklamas\u0131n\u0131 sa\u011flamak m\u00fcmk\u00fcn m\u00fcd\u00fcr?<\/p>\n
\u0130PUCU: Bu sorunun yan\u0131t\u0131, Hilbert Oteli\u2019nin \u00e7\u00f6z\u00fcm\u00fcne gider.<\/p>\n
Gelgelelim, Hilbert Oteli\u2019ni \u00e7\u00f6zmeye \u00e7al\u0131\u015fmak da eskilerin deyimiyle, abesle i\u015ftigaldir. Zira, Hilbert Oteli (ger\u00e7ek) evrenin par\u00e7as\u0131, unsuru de\u011fildir; eskilerin deyimiyle \u2018hay\u00e2l \u00e2lemi\u2019ne aittir.<\/p>\n
(*) https:\/\/plato.stanford.edu\/search\/searcher.py?query=frege
\nhttps:\/\/plato.stanford.edu\/search\/search?query=universal+set
\nhttps:\/\/www.jstor.org\/action\/doBasicSearch?Query=frege&so=rel
\nhttps:\/\/www.jstor.org\/action\/doBasicSearch?Query=universal+set&so=rel
\n(**) https:\/\/www.youtube.com\/watch?v=1DdN-RXSSlo<\/p>\n
Devam edece\u011fiz.<\/p>\n","protected":false},"excerpt":{"rendered":"
\u00d6n not: Konunun ilgilisi hayli uzun bir kaynak\u00e7a listesine sahiptir elbet. Yeni ilgilenebilecek okuyucu ise, \u015fu iki toplu kaynaktan se\u00e7im yapabilir. (*) \u00d6nceki pek \u00e7ok yaz\u0131m\u0131zda \u00e7e\u015fitli s\u00f6z\u00fcm ona paradokslara de\u011finmi\u015f idik. \u00d6rne\u011fin Zeno Paradokslar\u0131\u2019nda, g\u00f6r\u00fcn\u00fc\u015fteki zorlu\u011fun tamamen s\u00f6zc\u00fcklerden kaynakland\u0131\u011f\u0131n\u0131 de\u011ferlendirmi\u015ftik. \u0130kinci \u00f6rnek olarak de\u011ferlendirdi\u011fimiz Hilbert\u2019in Sonsuz Oteli (**) konusu hakk\u0131nda da pek \u00e7ok hem […]<\/p>\n","protected":false},"author":1425,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":"","_links_to":"","_links_to_target":""},"categories":[1],"tags":[],"class_list":["post-1071","post","type-post","status-publish","format-standard","hentry","category-genel"],"_links":{"self":[{"href":"https:\/\/blog.metu.edu.tr\/caglart\/wp-json\/wp\/v2\/posts\/1071","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/blog.metu.edu.tr\/caglart\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/blog.metu.edu.tr\/caglart\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/blog.metu.edu.tr\/caglart\/wp-json\/wp\/v2\/users\/1425"}],"replies":[{"embeddable":true,"href":"https:\/\/blog.metu.edu.tr\/caglart\/wp-json\/wp\/v2\/comments?post=1071"}],"version-history":[{"count":0,"href":"https:\/\/blog.metu.edu.tr\/caglart\/wp-json\/wp\/v2\/posts\/1071\/revisions"}],"wp:attachment":[{"href":"https:\/\/blog.metu.edu.tr\/caglart\/wp-json\/wp\/v2\/media?parent=1071"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/blog.metu.edu.tr\/caglart\/wp-json\/wp\/v2\/categories?post=1071"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/blog.metu.edu.tr\/caglart\/wp-json\/wp\/v2\/tags?post=1071"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}