Aristoteles<\/a>\u2019in Ar\u0131alytika prote-ra\u2019s\u0131nda (\u00d6n Analitikler) geli\u015ftirilmi\u015ftir. Bi\u00e7imsel mant\u0131\u011f\u0131n en eski dal\u0131d\u0131r.<\/p>\n\u00c7a\u011fda\u015f tas\u0131m kuram\u0131n\u0131n iki inceleme alan\u0131 vard\u0131r: Aristoteles\u2019in ele ald\u0131\u011f\u0131 ko\u015fulsuz (kategorik) tas\u0131m kuram\u0131 basit \u00f6nermelerle (tunlar\u0131n zorunluluk ya da olanakl\u0131l\u0131k bildiren kipliklerine (mod) g\u00f6re de\u011fi\u015fimlerini inceler. Ko\u015fulsuz olmayan tas\u0131m kuram\u0131 ise \u00f6nermeleri bir b\u00fct\u00fcn olarak birim alan mant\u0131ksal \u00e7\u0131kar\u0131m bi\u00e7imidir; k\u00f6keni Stoac\u0131 mant\u0131k\u00e7\u0131lara de\u011fin uzanmakla birlikte, John Neville Keynes\u2019in Studies and Exercises in<\/p>\n
Formal Logic (1884; Bi\u00e7imsel Mant\u0131k \u0130ncelemeleri ve Al\u0131\u015ft\u0131rmalar\u0131) adl\u0131 yap\u0131t\u0131n\u0131n yay\u0131mlanmas\u0131na de\u011fin tas\u0131m kuram\u0131n\u0131n ayr\u0131 bir kolu olarak g\u00f6r\u00fclmemi\u015ftir.<\/p>\n
Verilmi\u015f herhangi bir \u00f6nc\u00fcl ya da sonucun do\u011frulu\u011funu ya da yanl\u0131\u015fl\u0131\u011f\u0131n\u0131 bilmek \u00e7\u0131kar\u0131m\u0131n ge\u00e7erlili\u011fini belirlemeye yetmez. Bir kan\u0131tlaman\u0131n ge\u00e7erlili\u011fini anlayabilmek i\u00e7in onun mant\u0131ksal bi\u00e7imini kavramak gerekir. Bu sorunun ele al\u0131nd\u0131\u011f\u0131 geleneksel kategorik tas\u0131m kuram\u0131nda \u00f6nce t\u00fcm \u00f6nermeler d\u00f6rt temel bi\u00e7ime indirgenir.<\/p>\n
Her (bir) dir.<\/p>\n
Hi\u00e7bir (bir) de\u011fildir.<\/p>\n
Baz\u0131 (en az bir) (bir) dir.<\/p>\n
Baz\u0131 (bir) de\u011fildir.<\/p>\n
Bu bi\u00e7imler Latince affirmo (evetleme) ve nego (de\u011filleme) terimlerindeki \u00fcnl\u00fclerle, s\u0131ras\u0131yla A, E, \/ ve O \u00f6nermeleri olarak an\u0131l\u0131r. Evetleme ve de\u011filleme aras\u0131ndaki ayr\u0131m\u0131n niteliksel, ilk iki bi\u00e7imin t\u00fcmel kapsam\u0131yla son iki bi\u00e7imin tikel kapsam\u0131 aras\u0131ndaki ayr\u0131m\u0131n ise niceliksel oldu\u011fu kabul edilir.<\/p>\n
Yukar\u0131daki \u00f6nermelerde bo\u015fluklar\u0131 dolduran s\u00f6zc\u00fcklere \u201cterim\u201d denir. Bunlar tekil (\u00f6rn. Ay\u015fe) ya da genel (\u00f6rn. k\u0131zlar) olabilir. Genel terimlerin kullan\u0131m\u0131na ili\u015fkin \u00e7ok \u00f6nemli bir aynm, bunlann kaplam ve i\u00e7lemle-riyle ilgilidir. Kaplam, bir terimle anlat\u0131lan bireyler k\u00fcmesini, i\u00e7lem ise terimi tan\u0131mlayan nitelikler k\u00fcmesini belirtir. \u0130lk bo\u015flu\u011fu dolduran terim \u00f6nermenin \u00f6znesi, ikinci bo\u015flu\u011fu dolduran terim ise y\u00fcklemidir.<\/p>\n
20. y\u00fczy\u0131l ba\u015flar\u0131nda \u00fcnlenen mant\u0131k\u00e7\u0131 Jan Lukasiewicz\u2019in kulland\u0131\u011f\u0131 i\u015faret sisteminde genel terimler ya da ad simgeleri a, b ve c harfleriyle, \u00f6nerme bi\u00e7imlerini belirten d\u00f6rt tas\u0131m y\u00f6neticisi ise A, E, I ve O harfleriyle g\u00f6sterilir. Buna g\u00f6re, \u201cHer b, u\u2019d\u0131r\u201d \u00f6nermesi \u201cAba\u201d, \u201cBaz\u0131 6\u2019ler a\u2019d\u0131r\u201d \u00f6nermesi \u201cIha\u201d, \u201cHi\u00e7bir b. a de\u011fildir\u201d \u00f6nermesi \u201cEba\u201d ve \u201cBaz\u0131 h\u2019ler a de\u011fildir\u201d \u00f6nermesi \u201cOba\u201d bi\u00e7iminde yaz\u0131l\u0131r. Bu \u00f6nermeler aras\u0131ndaki ili\u015fkiler incelendi\u011finde a\u015fa\u011f\u0131daki \u00f6nermelerin t\u00fcm a ve b terimleri i\u00e7in do\u011fru oldu\u011fu g\u00f6r\u00fcl\u00fcr.<\/p>\n
Aba ve Eba ikisi birden de\u011fil.<\/p>\n
E\u011fer Aba ise, o halde iba.<\/p>\n
E\u011fer Eba ise, o halde Oba.<\/p>\n
Ya iba ya da Oba.<\/p>\n
Aba, Oban\u0131n de\u011fillemesine e\u015fde\u011ferdir.<\/p>\n
Eba, iba\u2019n\u0131n de\u011fillemesine e\u015fde\u011ferdir.<\/p>\n
Terimlerin s\u0131ras\u0131 tersine \u00e7evrilirse \u00f6nermenin \u201cbasit evri\u011fi\u201d elde edilir, ama bunun yan\u0131nda, bir A \u00f6nermesinin yerine I, ya da bir E \u00f6nermesinin yerine O \u00f6nermesi getirilirse ba\u015flang\u0131\u00e7taki \u00f6nermenin \u201cs\u0131n\u0131rl\u0131 evri\u011fi\u201d ortaya \u00e7\u0131kar. \u00d6nermelerle bunlann basit evrikleri aras\u0131nda \u00e7o\u011funlukla kar\u015f\u0131olum d\u00f6rtgeniyle g\u00f6sterilen mant\u0131ksal ili\u015fkiler \u015f\u00f6yledir: Eve l \u00f6nermeleri basit evrikleriyle e\u015fde\u011fer ya da e\u015fsay\u0131l\u0131d\u0131r (yani Eba ve \u0130ba, s\u0131ras\u0131yla Eab ve Iab\u2019yle \u00f6zde\u015ftir). Bir Aba \u00f6nermesi basit evri\u011fi Aab ile e\u015fde\u011fer olmasa da, s\u0131n\u0131rl\u0131 evri\u011fi Iab\u2019yi i\u00e7erir, ama onun taraf\u0131ndan i\u00e7erilmez. Conversio per accidens (ilineksel [rastlant\u0131sal] evirme) denen bu \u00e7\u0131kar\u0131m t\u00fcr\u00fc Eba\u2019n\u0131n Oab\u2019yi i\u00e7ermesi \u00f6rne\u011finde de ge\u00e7erlidir. Buna kar\u015f\u0131l\u0131k Oba Aab\u2019yi ne i\u00e7erir, ne de onun taraf\u0131ndan i\u00e7erilir; bu durum \u201cO \u00f6nermeleri evirilmez\u201d bi\u00e7iminde ifade edilir. Bir \u00f6nermenin, niteli\u011finin de\u011fi\u015ftirilmesiyle ikinci teriminin de-\u011fillenmesi sonucunda ortaya \u00e7\u0131kan \u00f6nermeyle e\u015fde\u011ferli\u011fine art\u00e7evirme denir. Son \u00e7\u0131kar\u0131m t\u00fcr\u00fc olan tamdevirme ise baz\u0131 \u00f6nermelerin, ad simgelerinin ikisi birden de\u011fillenerek s\u0131ralar\u0131 tersine \u00e7evrildi\u011finde ortaya \u00e7\u0131kan \u00f6nermeyi i\u00e7ermesinden \u00f6t\u00fcr\u00fc elde edilir.<\/p>\n
Ko\u015fulsuz tas\u0131m iki \u00f6nc\u00fclden bir sonu\u00e7 \u00e7\u0131kar\u0131lmas\u0131 anlam\u0131na gelir ve d\u00f6rt tan\u0131mlay\u0131c\u0131 niteli\u011fi vard\u0131r: 1) Her \u00fc\u00e7 \u00f6nerme A, E, I ya da O \u00f6nermesi bi\u00e7imindedir; 2) \u00e7\u0131kar\u0131m sonucunun \u00f6znesi (k\u00fc\u00e7\u00fck terim) \u00f6nc\u00fcllerden birinde (k\u00fc\u00e7\u00fck \u00f6nc\u00fcl) ge\u00e7er; 3) \u00e7\u0131kar\u0131m sonucunun y\u00fcklemi (b\u00fcy\u00fck terim) de \u00f6b\u00fcr \u00f6nc\u00fclde (b\u00fcy\u00fck \u00f6nc\u00fcl) ge\u00e7er; 4) \u00f6nc\u00fcllerde geriye kalan iki terimin yerinde tek bir terim (orta terim) yer al\u0131r. Bir tas\u0131mdaki \u00fc\u00e7 \u00f6nermeden her birinde nitelik ve niceli\u011fin d\u00f6rt bile\u015fiminden biri yer alabilece\u011fine g\u00f6re, ko\u015fulsuz tas\u0131mda 64 ayr\u0131 kip bulunabilir. Her kip d\u00f6rt bi\u00e7imin (\u00f6nermeler i\u00e7i terim dizili\u015fi) herhangi birinde ge\u00e7ebilir ve b\u00f6ylece 256 olas\u0131 bi\u00e7im elde edilir. Tas\u0131m kuram\u0131n\u0131n \u00f6nemli g\u00f6revlerinden biri de bu \u00e7ok say\u0131daki olas\u0131 bi\u00e7imi az say\u0131da ge\u00e7erli bi\u00e7ime indirgemektir.<\/p>\n
Aristoteles 14\u2019\u00fc ku\u015fkuya yer vermeyen, 5\u2019i de \u00e7ekince i\u00e7eren 19 ge\u00e7erli kip kabul eder. Bu 19 tas\u0131m\u0131n 5\u2019inin t\u00fcmel sonu\u00e7lan oldu\u011fundan, \u201cher\u201d ile ba\u015flayan \u00f6nermelerin \u201cbaz\u0131\u201d ile ba\u015flayan \u00f6nermelere d\u00f6n\u00fc\u015ft\u00fcr\u00fclmesiyle ge\u00e7erli kip say\u0131s\u0131 24\u2019e \u00e7\u0131kar\u0131labilir. Aristoteles, tan\u0131t\u0131n dolays\u0131z indirgeme, dolayl\u0131 indirgeme ya da reductio ad impossibile (olanaks\u0131za indirgeme) ile sa\u011fland\u0131\u011f\u0131 bir aksiyom sistemi kullanarak t\u00fcm tas\u0131mlan birinci bi\u00e7imin tas\u0131mlar\u0131na indirgemeyi ba\u015farm\u0131\u015ft\u0131r. G\u00fcn\u00fcm\u00fczde, terimleri \u201cbo\u015f k\u00fcme\u201d olup olmad\u0131klar\u0131na bakmaks\u0131z\u0131n kullanabilmek amac\u0131yla, tas\u0131m kuram\u0131 Boole cebirinin \u00f6zel bir bi\u00e7imi haline getirilmi\u015ftir. Bu t\u00fcr bir cebirde, s\u0131n\u0131f (k\u00fcme) bile\u015fim ve kesi\u015fim i\u015flemlerinin yan\u0131 s\u0131ra evrensel k\u00fcme ve bo\u015f k\u00fcme kavramlar\u0131 da kullan\u0131lmaktad\u0131r. Bu sistemle elde edilen 15 kip tas\u0131m kuram\u0131n\u0131n y\u00fcklemler mant\u0131\u011f\u0131nda yorumlanm\u0131\u015f teoremlerini olu\u015fturur.<\/p>\n
Ko\u015fulsuz olmayan tas\u0131mlar ya ko\u015fullu ya da tikel-evetlemeli olabilir; baz\u0131 yakla\u015f\u0131mlarda bunlara bir de ba\u011fla\u015f\u0131k tas\u0131mlar s\u0131n\u0131f\u0131 eklenir. Ko\u015fulsuz olmayan tas\u0131m kuram\u0131 ile ko\u015fulsuz tas\u0131m kuram\u0131 aras\u0131ndaki ba\u015fl\u0131ca fark, birincinin bile\u015fik terimleri inceleyen bir y\u00fcklemler mant\u0131\u011f\u0131, \u0130kincisinin ise analiz edilmemi\u015f tam \u00f6nermeleri birim alan bir \u00f6nermeler mant\u0131\u011f\u0131 olmas\u0131d\u0131r. Ko\u015fullu tas\u0131mda\u201c\/? Dq\u201d(p,q\u2019yu i\u00e7erir)bi\u00e7imindeki t\u00fcm \u00f6nermelere salt ad\u0131 verilir. \u0130ki ge\u00e7erli kipi bulunan karma ko\u015fullu tas\u0131mlarda ise bir ko\u015fullu ve bir ko\u015fulsuz \u00f6nc\u00fcl ile bir ko\u015fulsuz sonu\u00e7 vard\u0131r. \u201cYa\u2026 ya da \u2026\u201d bi\u00e7iminde bir y\u00f6neticiden olu\u015fan tikel-evetlemeli tas\u0131mlar\u0131n da iki \u00f6nemli kipi vard\u0131r. 20. y\u00fczy\u0131lda ko\u015fulsuz olmayan tas\u0131m kavram\u0131, karma\u015f\u0131k ve bile\u015fik \u00f6nermelerin yan\u0131nda kurucu ve y\u0131k\u0131c\u0131 kipleriyle ikilemleri de i\u00e7ine alacak bi\u00e7imde geni\u015fletilmi\u015ftir.<\/p>\n","protected":false},"excerpt":{"rendered":"
Tas\u0131m, K\u0131yas olarak da bilinir, mant\u0131kta, iki \u00f6nc\u00fcl ve bir sonu\u00e7tan olu\u015fan t\u00fcmdengelimli ge\u00e7erli kan\u0131tlama. En genel bi\u00e7imi, her birinin iki kez kullan\u0131ld\u0131\u011f\u0131 \u00fc\u00e7 terimli ko\u015fulsuz tas\u0131md\u0131r: \u201cHer insan \u00f6l\u00fcml\u00fcd\u00fcr;…<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[92],"tags":[3032,3030,3031],"class_list":["post-8309","post","type-post","status-publish","format-standard","hentry","category-bilim","tag-kiyas","tag-mantik","tag-tasim"],"_links":{"self":[{"href":"https:\/\/www.ilkkimbuldu.com\/index.php?rest_route=\/wp\/v2\/posts\/8309"}],"collection":[{"href":"https:\/\/www.ilkkimbuldu.com\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.ilkkimbuldu.com\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.ilkkimbuldu.com\/index.php?rest_route=\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.ilkkimbuldu.com\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=8309"}],"version-history":[{"count":4,"href":"https:\/\/www.ilkkimbuldu.com\/index.php?rest_route=\/wp\/v2\/posts\/8309\/revisions"}],"predecessor-version":[{"id":11818,"href":"https:\/\/www.ilkkimbuldu.com\/index.php?rest_route=\/wp\/v2\/posts\/8309\/revisions\/11818"}],"wp:attachment":[{"href":"https:\/\/www.ilkkimbuldu.com\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=8309"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.ilkkimbuldu.com\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=8309"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.ilkkimbuldu.com\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=8309"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}