\nTarihsel Geli\u015fim: <\/p>\n
\u201cT\u00fcmdengelim\u201d y\u00f6ntemi mant\u0131kta, bir yada daha fazla \u00f6nc\u00fclden zorunlu olarak sonucun \u00e7\u0131kar\u0131lmas\u0131d\u0131r ve t\u00fcmelle tikel (genelle \u00f6zel) aras\u0131nda s\u0131k\u0131 bir ili\u015fki g\u00f6ren ve bu ili\u015fkiyi en do\u011fru olarak ortaya koyman\u0131n yollar\u0131n\u0131 ara\u015ft\u0131ran Aristotales\u2019in bulu\u015fudur. <\/p>\n
Aristotales, antik\u00e7a\u011f Yunan d\u00fc\u015f\u00fcncesinde \u00e7a\u011fda\u015f anlam\u0131yla ilk bilgindir. Kendisinden \u00f6nce b\u00fct\u00fcn bilgileri toplam\u0131\u015f, i\u00e7 i\u00e7e ge\u00e7mi\u015f olanlar\u0131 birbirinden ay\u0131rm\u0131\u015f, s\u0131n\u0131fland\u0131rm\u0131\u015f, ele\u015ftirmi\u015f ve b\u00fct\u00fcnlemeye \u00e7al\u0131\u015fm\u0131\u015ft\u0131r. \u00d6zellikle sonradan Metafizik ad\u0131 verilen Prote Filosofia (\u0130lk felsefe) adl\u0131 yap\u0131t\u0131 Thales’den kendisine kadar glen felsefe tarihinin \u00e7ok ba\u015far\u0131l\u0131 bir \u00f6zetidir ve en g\u00fcvenilir kayna\u011f\u0131d\u0131r. Toplad\u0131\u011f\u0131 bilgilerin do\u011fruluklar\u0131n\u0131 \u00f6l\u00e7mek i\u00e7in bilimsel bir d\u00fc\u015f\u00fcnme y\u00f6ntemi aram\u0131\u015f ve do\u011fru d\u00fc\u015f\u00fcnmenin kurallar\u0131n\u0131 b\u00fct\u00fcn ayr\u0131nt\u0131lar\u0131yla saptamaya \u00e7al\u0131\u015farak bunlara do\u011fru d\u00fc\u015f\u00fcnmenin aletleri anlam\u0131na gelen organon ad\u0131n\u0131 vermi\u015ftir. Aristotalesin bu do\u011fru d\u00fc\u015f\u00fcnme kurallar\u0131na sonradan mant\u0131k ad\u0131 verilmi\u015ftir. <\/p>\n
Gen\u00e7 Aristotales hen\u00fcz Akademia’da bir Platon \u00f6\u011frencisi iken kendisine kadar gelen d\u00fc\u015f\u00fcnmede \u00fc\u00e7 bak\u0131\u015f bulunuyordu: \u0130nsan\u0131n g\u00f6r\u00fcnene bak\u0131\u015f\u0131 (do\u011fa), insan\u0131n kendisine bak\u0131\u015f\u0131 (insan) ve insan\u0131n g\u00f6r\u00fcnmeyene bak\u0131\u015f\u0131 (do\u011fa \u00fcst\u00fc)… D\u00fc\u015f\u00fcn\u00fcr Aristotales y\u00f6ntemsel aletler bularak bu ilkel bak\u0131\u015f\u0131 do\u011fru bak\u0131\u015fa \u00e7evirmek istedi: G\u00f6r\u00fcnmeyenden g\u00f6r\u00fcnene bakmak (t\u00fcmdengelim “do\u011frulama”) g\u00f6r\u00fcnenden g\u00f6r\u00fcnmeyene bakmak (t\u00fcmevar\u0131m “ara\u015ft\u0131rma”)…<\/p>\n
Ne varki bu do\u011fru bak\u0131\u015f\u0131 ger\u00e7ekle\u015ftirmek i\u00e7in d\u00fc\u015f\u00fcnmenin bilimden yararlanmas\u0131, e\u015fdeyi\u015fle d\u00fc\u015f\u00fcnce-do\u011fabilim diyalekti\u011fi gerekiyordu. O \u00e7a\u011f\u0131n bilimleriyse d\u00fc\u015f\u00fcnmenin pek gerisindeydiler. Bu y\u00fczdendir ki d\u00fc\u015f\u00fcn\u00fcr Aristotales, d\u00fc\u015f\u00fcnmesine kar\u015f\u0131l\u0131k verecek bilimi de kendisi yapmak zorundayd\u0131. \u00c7e\u015fitli bilim alanlar\u0131ndaki, \u00e7a\u011f\u0131n\u0131n \u00f6l\u00e7\u00fclerine g\u00f6re pek geni\u015f, bilimsel \u00e7abalar\u0131n\u0131n nedeni budur. Bu bilimsel \u00e7al\u0131\u015fmalardan ve bu \u00e7al\u0131\u015fmalar s\u0131ras\u0131nda ilk felsefe (prote filosofia) do\u011fdu. Art\u0131k \u00e7a\u011f\u0131yla zorunlu imkanlar i\u00e7inde, geleneksel b\u00fcy\u00fck soruya kar\u015f\u0131l\u0131k aranacakt\u0131r: \u0130lkneden nedir?… \u0130lkneden en son ve en geli\u015fmi\u015f, Platon’un ideas\u0131 olamaz. \u00c7\u00fcnk\u00fc idea g\u00f6r\u00fcnen say\u0131s\u0131z ger\u00e7ek bi\u00e7imlerinin i\u00e7indedir ve o bi\u00e7imlerden soyularak, e\u015fdeyi\u015fle i\u00e7lerinden \u00e7\u0131kar\u0131larak elde edilmi\u015ftir. Kald\u0131 ki Platon, bu idealara nesnelere \u00f6z\u00fc demektedir, \u00f6yleyse \u00f6z nas\u0131l bi\u00e7imsel nesneden ayr\u0131 ve onun d\u0131\u015f\u0131nda olabilir? \u00d6z’s\u00fcz bi\u00e7im ve bi\u00e7im’siz \u00f6z olamaz. <\/p>\n
\u00d6yleyse g\u00f6r\u00fcnenden g\u00f6r\u00fcnmeyene bak\u0131p ara\u015ft\u0131rmal\u0131y\u0131z ama buldu\u011fumuzu da g\u00f6r\u00fcnmeyenden g\u00f6r\u00fcnene bak\u0131p (t\u00fcmdengelim) do\u011frulamal\u0131y\u0131z. T\u00fcmevar\u0131mla ara\u015ft\u0131r\u0131p ideay\u0131 buluyoruz, \u015fimdi onu t\u00fcmdengelimle do\u011fru yerine oturtmal\u0131y\u0131z. <\/p>\n
Genelden \u00f6zele inen t\u00fcmdengelim y\u00f6ntemi ile \u00f6zelden genele \u00e7\u0131kan t\u00fcmevar\u0131m y\u00f6ntemi 17. Y\u00fczy\u0131ldan itibaren bir hayli geli\u015ftirilmi\u015ftir. \u00d6zellikle bu iki y\u00f6ntem aras\u0131ndaki ba\u011fl\u0131l\u0131k, ikisinin birlikte kullan\u0131lmas\u0131 diyalektik mant\u0131kla ger\u00e7ekle\u015fmi\u015ftir. <\/p>\n
19. ve 20. y\u00fczy\u0131llarda matematiksel mant\u0131\u011f\u0131n problemlerine ili\u015fkin ara\u015ft\u0131rmalar t\u00fcmdengelimle ba\u011f\u0131nt\u0131l\u0131 nosyonlara a\u00e7\u0131kl\u0131k kazand\u0131rm\u0131\u015f ve genelden \u00f6zele bir ded\u00fcksiyon, olarak t\u00fcmdengelim kavram\u0131n\u0131n yetersizli\u011fini g\u00f6stermi\u015ftir. Modern t\u00fcmevar\u0131m kavram\u0131 Aristotales\u2019\u00e7i sillojistik t\u00fcmdengelim (genelden \u00f6zele) yorumunun geni\u015f \u00e7apl\u0131 bir genelle\u015ftirilmesidir. Dar olarak, t\u00fcmdengelim, herhangi bir t\u00fcmdengelimi veya \u00e7\u0131karsamay\u0131 belirtir. <\/p>\n
Tan\u0131mlamalar: <\/p>\n
Kesin sonu\u00e7 veren ak\u0131l y\u00fcr\u00fctmeye \u00e7\u0131kar\u0131m, ded\u00fcksiyon (t\u00fcmdengelim) denir. Bu y\u00f6nteme g\u00f6re, do\u011fan\u0131n ara\u015ft\u0131r\u0131lmas\u0131 \u00f6nce g\u00f6zlemlerden genel prensiplerin \u00e7\u0131kar\u0131lmas\u0131 (t\u00fcmevar\u0131m) ve daha sonra genel prensiplere dayanarak g\u00f6zlemlerin a\u00e7\u0131klanmas\u0131 (t\u00fcmdengelim) a\u015famalar\u0131n\u0131 i\u00e7ermektedir. <\/p>\n
T\u00fcmdengelim; t\u00fcmelden tikeli ve genelden \u00f6zeli \u00e7\u0131karan uslamlama y\u00f6ntemidir. T\u00fcmdengelim, do\u011fru olan ya da do\u011fru oldu\u011fu san\u0131lan \u00f6nermelerden zorunlu olarak \u00e7\u0131kan yeni \u00f6nermeler t\u00fcretir. \u00d6nc\u00fcller do\u011fruysa sonu\u00e7 da mant\u0131ksal bir zorunlulukla do\u011frudur. <\/p>\n
Zihnin kanunlardan, kurallara \u00f6rneklere, olaylara inerek yeni bir yarg\u0131da bulunmas\u0131d\u0131r. T\u00fcmevar\u0131m\u0131n tersine, genel ilkelerden \u00f6zel durumlara inen bir ak\u0131l y\u00fcr\u00fctme \u015feklidir. Burada herhangi bir genelleme (kanun, kural) ele al\u0131n\u0131r, sonra bundan yola \u00e7\u0131karak \u00f6zele (olaya, \u00f6rne\u011fe) inilerek, yeni bir yarg\u0131ya var\u0131l\u0131r. <\/p>\n
T\u00fcmdengelim, bir ya da birden \u00e7ok \u00f6nc\u00fclden mant\u0131k kanunlar\u0131na g\u00f6re, bir sonu\u00e7lama (netice) ispatlay\u0131\u015f yada \u00e7\u0131karsay\u0131\u015f i\u015flemidir. <\/p>\n
T\u00fcmdengelimle var\u0131lan bir sonu\u00e7, bir \u00f6nermeler zinciridir ki, burada, \u00f6nermelerin mant\u0131k kanunlar\u0131yla do\u011frudan do\u011fruya \u00e7\u0131kar\u0131lan bir \u00f6nc\u00fcl yada bir \u00f6nermedir. T\u00fcmdengelimle var\u0131lan bir sonu\u00e7lamada, neticeler \u00f6nc\u00fcllerde sakl\u0131d\u0131r, mant\u0131ksal analiz metotlar\u0131yle \u00e7\u0131karsanmalar\u0131 icap eder. T\u00fcmdengelimin temelinde \u201cb\u00fct\u00fcn i\u00e7in do\u011fru olan, par\u00e7alar\u0131 i\u00e7in de do\u011frudur\u201d ilkesi yatar. <\/p>\n
\u00d6\u011fretimde T\u00fcmdengelim: <\/p>\n
\u00d6\u011frenilmi\u015f olan genel bilgilerden yeni bilgiler elde etmede kullan\u0131lan transfer (ge\u00e7i\u015f) \u00f6\u011fretimde, t\u00fcmdengelime iyi \u00f6rnek te\u015fkil eder. \u00d6\u011fretimde transfer, ge\u00e7mi\u015fte \u00f6\u011frenmi\u015f oldu\u011fumuz bilgi ve tecr\u00fcbelerin yeni bilgi ve beceriler elde etmemize uygulanmas\u0131 ve bunu kolayla\u015ft\u0131rmas\u0131 olay\u0131d\u0131r. Bu anlamda transfer konular\u0131n benzerliklerine, y\u00f6ntemlerine, ilkelerine ait olmak \u00fczere \u00fc\u00e7 \u015fekilde uygulan\u0131r. \u0130\u015fte \u00f6\u011frendiklerimizin transferi yap\u0131l\u0131rken genelliklerden yeni ve \u00f6zel durumlara ge\u00e7i\u015f \u015feklinde uygulan\u0131yorsa bu, \u00f6\u011fretimde bir t\u00fcmdengelimdir. <\/p>\n
T\u00fcmdengelimsel Metot: <\/p>\n
T\u00fcmdengelimsel Metot, yaln\u0131zca t\u00fcmdengelimsel tekniklere dayanan bir bilimsel \u00e7\u0131karsama metodudur. Felsefede t\u00fcmdengelimsel metot ve di\u011fer metotlar aras\u0131nda ay\u0131r\u0131c\u0131 bir \u00e7izgi \u00e7izme ve t\u00fcmdengelimsel muhakemeyi tecr\u00fcbenin d\u0131\u015flanmas\u0131 ve bilimde t\u00fcmdengelime a\u015f\u0131r\u0131 \u00f6nem verilmesi olarak tan\u0131mlama hususunda giri\u015fimlerde bulunulmu\u015ftur. Fakat t\u00fcmdengelim ve t\u00fcmevar\u0131m aras\u0131nda kar\u015f\u0131l\u0131kl\u0131 ba\u011f\u0131nt\u0131 vard\u0131r ve t\u00fcmevar\u0131msal muhakeme insano\u011flunun y\u00fczy\u0131llarca s\u00fcren pratiksel ve bilgisel \u00e7abas\u0131na dayal\u0131d\u0131r. T\u00fcmdengelimsel metot, genel olarak ampirik verilerin, bunlar\u0131n biriki\u015finden ve teorik bi\u00e7imde yorumlan\u0131\u015f\u0131ndan sonra, uygun b\u00fct\u00fcn sonu\u00e7lar\u0131 daha tam ve daha tutarl\u0131 bi\u00e7imde \u00e7\u0131karsamak amac\u0131yla sistemle\u015ftirilmesinde kullan\u0131lan ge\u00e7erli bilimsel \u00e7\u0131karsama metotlar\u0131ndan birisidir. Bu metot yeni bilgiyi, di\u011fer \u015feyler aras\u0131nda, ded\u00fcktif bir tarzda form\u00fcle edilmi\u015f olan bir teorinin m\u00fcmk\u00fcn yorumlar\u0131n\u0131n bir toplam\u0131 kabul eder. <\/p>\n
T\u00fcmdengelim Teoremi: <\/p>\n
Mant\u0131k \u00f6tesi anahtar bir terim ki \u015fu demektir: e\u011fer B \u00f6nermesi, A \u00f6nc\u00fcl\u00fcn\u00fcn de do\u011fru oldu\u011fu varsay\u0131m\u0131 (assumption) \u00fczerinde \u00e7\u0131karsanm\u0131\u015fsa, o takdirde, (A muteberdir) varsay\u0131m\u0131 olmaks\u0131z\u0131n, belirli say\u0131da \u00f6nc\u00fcllerden, mademki A vard\u0131r, \u00f6yleyse B\u2019 de vard\u0131r sonucu \u00e7\u0131kar\u0131labilir. T\u00fcmdengelim Teoremi \u00f6nemli muhtelif mant\u0131ksal sistemlere uygulanmaktad\u0131r, klasik ve konstr\u00fcktif \u00f6nermeler ve y\u00fcklemler hesab\u0131, formel aritmetik vb. T\u00fcmdengelim teoremi, baz\u0131 sistemler i\u00e7in, \u00f6rne\u011fin belirli modal mant\u0131k sistemleri i\u00e7in ge\u00e7erli de\u011fildir. T\u00fcmdengelim teoremi formalize edilmi\u015f-olmayan muhakemede geni\u015f bi\u00e7imde kullan\u0131l\u0131r. T\u00fcmdengelim teoremi ispat s\u00fcrecini basitle\u015ftirir. O, ilk olarak tek bir sistem i\u00e7in, Jacques Herbrand taraf\u0131ndan tan\u0131mlanm\u0131\u015f ve ispat edilmi\u015f ve genel bir metodolojik ilke olarak 1932\u2019de Tarski taraf\u0131ndan form\u00fcllendirilmi\u015ftir. <\/p>\n
\u00d6rneklerle Ded\u00fcksiyon (Ded\u00fcktif \u00c7\u0131kar\u0131m, T\u00fcmdengelim):<\/p>\n
\u00d6rnek: (1) \u201cinsanlar \u00f6l\u00fcml\u00fcd\u00fcr – Sokrates insand\u0131r – \u00d6yleyse Sokrates’de \u00f6l\u00fcml\u00fcd\u00fcr\u201d tas\u0131m\u0131, t\u00fcmdengelen bir tas\u0131md\u0131r. B\u00fct\u00fcn insanlar\u0131n \u00f6l\u00fcml\u00fc olduklar\u0131 do\u011fruysa Sokrates’de bir insan oldu\u011funa g\u00f6re Sokrates\u2019in de \u00f6l\u00fcml\u00fc olmas\u0131 zorunludur, ba\u015fka t\u00fcrl\u00fc olamaz. Ancak kimi mant\u0131k\u00e7\u0131lar t\u00fcmdengelimin yeni bir bilgi vermedi\u011fini, bunun bir genelleme (totoloji) oldu\u011funu, \u00e7\u00fcnk\u00fc Sokrates\u2019in \u00f6l\u00fcml\u00fcl\u00fc\u011f\u00fcn\u00fcn esasen Sokrates\u2019in insanl\u0131\u011f\u0131nda i\u00e7kin bulundu\u011funu ileri s\u00fcrm\u00fc\u015flerdir.<\/p>\n
\u00d6rnek (1)<\/p>\n
\u0130nsanlar \u00f6l\u00fcml\u00fcd\u00fcr.
\nSokrates insand\u0131r.
\n_______________
\nO halde Sokrates \u00f6l\u00fcml\u00fcd\u00fcr.<\/p>\n
Mant\u0131\u011f\u0131n ana konusunu, ge\u00e7erli ak\u0131l y\u00fcr\u00fctmeler s\u0131n\u0131rland\u0131rmaktad\u0131r. \u00dc\u00e7 ak\u0131l y\u00fcr\u00fctme t\u00fcr\u00fc (ded\u00fcksiyon, end\u00fcksiyon, analoji) i\u00e7erisinde, \u00f6nc\u00fcllerin do\u011fru kabul edilmesi halinde sonucun bu \u00f6nc\u00fcllerden zorunlu olarak \u00e7\u0131kt\u0131\u011f\u0131 yani ge\u00e7erli olabilen bir tek ak\u0131l t\u00fcr\u00fc vard\u0131r ki, buna ded\u00fcksiyon, ded\u00fcktif ak\u0131l y\u00fcr\u00fctme veya t\u00fcmdengelim denir. \u00d6b\u00fcr iki ak\u0131l y\u00fcr\u00fctme t\u00fcr\u00fc (end\u00fcksiyon ve anoloji) ge\u00e7erli ak\u0131l y\u00fcr\u00fctmeler i\u00e7ermez. Mant\u0131\u011f\u0131 yaln\u0131zca ge\u00e7erli ak\u0131l y\u00fcr\u00fctmelerle ilgilenen bir disiplin olarak s\u0131n\u0131rland\u0131rd\u0131\u011f\u0131m\u0131zda, bu durumda mant\u0131\u011f\u0131n temel konusunun ded\u00fcksiyonlar olaca\u011f\u0131 a\u00e7\u0131kt\u0131r ve baz\u0131 mant\u0131k\u00e7\u0131lar\u0131n mant\u0131\u011f\u0131 ded\u00fcktif mant\u0131k olarak adland\u0131rmalar\u0131n\u0131n gerek\u00e7esi de budur.<\/p>\n
\u00d6rnek (2)<\/p>\n
T\u00fcm A\u2019lar B\u2019dir.
\nX bir A\u2019d\u0131r.
\n_______________
\nO halde, X bir B\u2019dir.<\/p>\n
\u0130\u015fte, bu forma uygun t\u00fcm ak\u0131l y\u00fcr\u00fctmeler birer ded\u00fcksiyondur. Ba\u015fka bir deyi\u015fle, form ge\u00e7erli oldu\u011fundan, bu forma uygun t\u00fcm somut \u00f6rnekler de ge\u00e7erlidir. End\u00fcksiyon ve anolojinin ge\u00e7ersiz ak\u0131l y\u00fcr\u00fctmeler oldu\u011fu belirtilmi\u015fti. Bunun gerek\u00e7eleri, a\u015fa\u011f\u0131da bu iki ak\u0131l y\u00fcr\u00fctme t\u00fcr\u00fc \u00fczerinde dururken a\u00e7\u0131klanacakt\u0131r. Ama burada hemen saptanabilecek \u015fudur ki, bir ak\u0131l y\u00fcr\u00fctme ge\u00e7erli ise, o bir ded\u00fcksiyondur. Ne var ki, bunun tersi do\u011fru de\u011fildir. A\u015fa\u011f\u0131daki \u00f6rne\u011fe bakal\u0131m.<\/p>\n
\u00d6rnek (3)<\/p>\n
Baz\u0131 d\u00f6rt ayakl\u0131lar kedidir.
\nB\u00fct\u00fcn atlar d\u00f6rt ayakl\u0131d\u0131r.
\n______________________
\nO halde, baz\u0131 atlar kedidir.<\/p>\n
Bu ded\u00fcksiyon ge\u00e7erli de\u011fildir. \u00c7\u00fcnk\u00fc baz\u0131 \u201cd\u00f6rt ayakl\u0131lar\u201d\u0131n \u201ckedi\u201d olmas\u0131, b\u00fct\u00fcn \u201catlar\u0131n\u201d \u201cd\u00f6rt ayakl\u0131\u201d olmas\u0131ndan dolay\u0131 baz\u0131 atlar\u0131n kedi olmas\u0131n\u0131 zorunlu k\u0131lmaz. Burada bir ded\u00fcksiyonu ge\u00e7erli k\u0131lan baz\u0131 kurallar\u0131n bulundu\u011funu tahmin edebiliriz. Her ded\u00fcksiyon ge\u00e7erli de\u011fildir; ama her ge\u00e7erli ak\u0131l y\u00fcr\u00fctme bir ded\u00fcksiyondur. <\/p>\n
Ge\u00e7erli bir ded\u00fcksiyona bakt\u0131\u011f\u0131m\u0131zda, b\u00f6yle bir ded\u00fcksiyonun bir \u00e7\u0131kar\u0131m oldu\u011funu g\u00f6r\u00fcr\u00fcz. \u00c7\u00fcnk\u00fc ge\u00e7erli bir ded\u00fcksiyonda, sonu\u00e7 \u00f6nc\u00fcllerin i\u00e7inde zaten \u00f6rt\u00fck veya sakl\u0131 olarak vard\u0131r. \u00d6rne\u011fin \u201cB\u00fct\u00fcn insanlar \u00f6l\u00fcml\u00fcd\u00fcr; Sokrates bir insand\u0131r; o halde Sokrates \u00f6l\u00fcml\u00fcd\u00fcr\u201d gibi ge\u00e7erli bir ded\u00fcksiyonda, Sokrates\u2019in \u00f6l\u00fcml\u00fc oldu\u011funu bildiren sonu\u00e7 \u00f6nermesi, zaten \u201cB\u00fct\u00fcn insanlar \u00f6l\u00fcml\u00fcd\u00fcr\u201d \u00f6nc\u00fcl \u00f6nermesinde \u00f6rt\u00fck ve sakl\u0131 olarak bulunmaktad\u0131r. Bu nedenle, ded\u00fcksiyon, \u00f6nc\u00fcllerde \u00f6rt\u00fck veya sakl\u0131 halde bulunan\u0131 a\u00e7\u0131\u011fa \u00e7\u0131karma, \u00f6rt\u00fcy\u00fc kald\u0131rma i\u015flemi olarak kendini g\u00f6sterir. Ded\u00fcksiyonun bu niteli\u011fi bilgi a\u00e7\u0131s\u0131ndan felsefe tarihi i\u00e7erisinde bir ele\u015ftiri konusu olmu\u015f ve ded\u00fcksiyonun bize yeni bir bilgi vermedi\u011fi, eldeki bilgiyi yineledi\u011fi s\u00f6ylenmi\u015ftir. Ger\u00e7ekten de, ded\u00fcksiyonda, sonu\u00e7 \u00f6nermesi, i\u00e7erik bak\u0131m\u0131ndan \u00f6nc\u00fcllere ne yeni bir \u015fey katar, ne de bu \u00f6nc\u00fcllerin i\u00e7eri\u011fini a\u015fan yeni bir \u015fey bildirir. Tekrar vurgulamak gerekirse, ded\u00fcksiyonun i\u015flevi, \u00f6nc\u00fcllerde zaten sakl\u0131 veya \u00f6rt\u00fck olarak i\u00e7erilmi\u015f olan\u0131 sonu\u00e7 \u00f6nermesinde a\u00e7\u0131\u011fa \u00e7\u0131karmaktan ibarettir. Bu nedenle ded\u00fcksiyona bilgilerimizi art\u0131r\u0131c\u0131, denetleyici bir ak\u0131l y\u00fcr\u00fctme t\u00fcr\u00fc olarak bakmak uygun olur.Ancak ded\u00fcksiyonun esas \u00f6nemi ve i\u015flevi, bilgilerimizi bir kuram ve hatta sistem i\u00e7erisinde d\u00fczenlememize elveren, kan\u0131tlay\u0131c\u0131 \u00f6zelli\u011findedir. Bilimler kadar matematik ve felsefe de, ded\u00fcksiyonun bu \u00f6zelli\u011finden yararlan\u0131rlar.<\/p>\n
Burada \u201cded\u00fcksiyon\u201d terimi ile ilgili terminolojik saptama yapmak da gerekli g\u00f6r\u00fclmektedir.T\u00fcrk\u00e7ede bu terime kar\u015f\u0131l\u0131k olarak t\u00fcmdengelim terimi \u00f6nerilmi\u015f ve benimsenmi\u015ftir. Ancak, t\u00fcmdengelim terimi, b\u00fct\u00fcn par\u00e7a ili\u015fkisini \u00e7a\u011fr\u0131\u015ft\u0131rmakta, b\u00fct\u00fcnden par\u00e7aya do\u011fru bir gidi\u015fi sezinletmektedir. Oysa her ded\u00fcksiyon bir t\u00fcmdengelim de\u011fildir. \u00d6rne\u011fin, \u201ct\u00fcm A\u2019lar B\u2019dir\u201d ve \u201ct\u00fcm B\u2019ler C\u2019dir\u201d \u00f6nc\u00fcllerinden \u201ct\u00fcm A\u2019lar C\u2019dir\u201d sonucunu elde etti\u011fimizde, burada bir \u201ct\u00fcmden gelme\u201d yoktur; \u201ct\u00fcmden t\u00fcme ge\u00e7me\u201d vard\u0131r. Ama bunun yan\u0131s\u0131ra, (1) numaral\u0131 \u00f6rne\u011fimiz bir t\u00fcmdengelimdir. \u00c7\u00fcnk\u00fc bu \u00f6rnekte \u201ct\u00fcm\u201d\u00fcn i\u00e7inden bir par\u00e7ay\u0131, sonu\u00e7 \u00f6nermesi halinde elde ediyoruz. O halde t\u00fcmdengelim terimi ded\u00fcksiyon terimini k\u0131smen kar\u015f\u0131lamaktad\u0131r veya t\u00fcmdengelim terimi baz\u0131 ded\u00fcksiyonlar\u0131 adland\u0131rmakta kullan\u0131labilir. <\/p>\n
Bir arg\u00fcmanda \u00f6nc\u00fcller do\u011fru ve sonu\u00e7 i\u00e7in yeterli ise, sonucun yanl\u0131\u015f olmas\u0131 olanaks\u0131zd\u0131r. O halde sonucun do\u011frulu\u011funun ispat\u0131 hem t\u00fcm \u00f6nc\u00fcllerin do\u011fru olmas\u0131n\u0131, hem de \u00f6nc\u00fcllerin sonucu zorunlu k\u0131lmas\u0131n\u0131 gerektirir. Ancak \u00f6nc\u00fcllerin do\u011frulu\u011funun saptanmas\u0131 mant\u0131ksal sorun olmad\u0131\u011f\u0131ndan ne zaman tam bir ispata ula\u015ft\u0131\u011f\u0131m\u0131z kesinlikle bilinemez. Mant\u0131k\u00e7\u0131, \u00f6nc\u00fclleri \u201cdo\u011fru saymak\u201dla i\u015fe ba\u015flar. Onu as\u0131l ilgilendiren, bunlar\u0131 do\u011fru sayd\u0131\u011f\u0131na g\u00f6re daha neyi do\u011fru saymas\u0131d\u0131r. Do\u011fru say\u0131lan \u015fey veya \u015feyler yanl\u0131\u015f da olabilir. Fillerin u\u00e7tu\u011funu, \u00f6n\u00fcmdeki kitab\u0131n da fil oldu\u011funu kabul ediyorsam, kitab\u0131n u\u00e7tu\u011funu da kabul etmek zorunday\u0131m. Bu zorunluluk sadece arg\u00fcman\u0131n mant\u0131ksal y\u00f6nden ge\u00e7erli oldu\u011funu g\u00f6sterir; yoksa sonucun do\u011frulu\u011funun ispat\u0131n\u0131 de\u011fil. Arg\u00fcman\u0131n ge\u00e7erli olmas\u0131 sonucun ispat\u0131 i\u00e7in gerekli ancak yeterli de\u011fildir. \u00d6nc\u00fcllerin do\u011fru olmas\u0131 gere\u011fi de vard\u0131r. <\/p>\n
G\u00f6r\u00fcl\u00fcyor ki, bir arg\u00fcman\u0131n ge\u00e7erli\u011fi ile arg\u00fcman\u0131 olu\u015fturan do\u011fruluk de\u011feri aras\u0131nda bir ili\u015fki yoktur. Ge\u00e7erlik bu \u00f6nermelerin arg\u00fcmandaki ili\u015fkilerinin bir \u00f6zelli\u011fidir. E\u011fer sonucun \u00f6nc\u00fcllerle olan ili\u015fkisi, \u00f6nc\u00fclleri do\u011fru sayd\u0131\u011f\u0131m\u0131zda sonucu da do\u011fru saymam\u0131z\u0131 zorunlu k\u0131l\u0131c\u0131 nitelikte ise, arg\u00fcman ge\u00e7erli demektir. Arg\u00fcman\u0131n ge\u00e7erli olmas\u0131 ne \u00f6nc\u00fcllerin, ne de sonucun do\u011fru oldu\u011funu g\u00f6sterir; sadece arg\u00fcman\u0131n ge\u00e7erli bir \u00e7\u0131kar\u0131m bi\u00e7imine ba\u011fl\u0131 oldu\u011funu g\u00f6sterir. <\/p>\n
Do\u011fruluk ile ge\u00e7erlik aras\u0131ndaki ili\u015fkiyi ya da ili\u015fkisizli\u011fi daha fazla a\u00e7\u0131kl\u0131\u011fa kavu\u015fturmak i\u00e7in \u015fu \u00fc\u00e7 noktay\u0131 belirtmek yerinde olur:<\/p>\n
Verilen bir arg\u00fcman\u0131n ge\u00e7erli ve \u00f6nc\u00fcllerinin do\u011fru oldu\u011funu biliyorsak, sonucun do\u011fru oldu\u011funu kesinlikle s\u00f6yleyebiliriz.
\nVerilen bir arg\u00fcman ge\u00e7erli ve \u00e7\u0131kar\u0131lan sonu\u00e7 yanl\u0131\u015fsa, \u00f6nc\u00fcllerden hi\u00e7 de\u011filse birinin yanl\u0131\u015f oldu\u011funu kesinlikle s\u00f6yleyebiliriz.
\nVerilen bir arg\u00fcmanda t\u00fcm \u00f6nc\u00fcllerin do\u011fru, sonucun ise yanl\u0131\u015f oldu\u011funu biliyorsak, arg\u00fcman\u0131n ge\u00e7ersiz oldu\u011funu kesinlikle s\u00f6yleyebiliriz. <\/p>\n
Her \u00fc\u00e7 halde de dayand\u0131\u011f\u0131m\u0131z temel ilke, do\u011fru \u00f6nc\u00fcllerden yanl\u0131\u015f bir sonucun ge\u00e7erli olarak \u00e7\u0131kar\u0131lamayaca\u011f\u0131d\u0131r. Bu, ku\u015fkusuz, yanl\u0131\u015f \u00f6nc\u00fcllerden do\u011fru veya yanl\u0131\u015f bir sonucun ge\u00e7erli olarak \u00e7\u0131kar\u0131lamayaca\u011f\u0131 anlam\u0131na gelmez.<\/p>\n
Ancak \u00f6nermelerin do\u011fruluk de\u011ferini saptama mant\u0131k\u00e7\u0131ya d\u00fc\u015fmedi\u011fine g\u00f6re, onun g\u00f6revi arg\u00fcmanlar\u0131n ge\u00e7erli olup olmad\u0131\u011f\u0131n\u0131 saptamakla s\u0131n\u0131rl\u0131 demektir. O birtak\u0131m \u00e7\u0131kar\u0131m kurallar\u0131na ba\u015fvurarak ge\u00e7erli arg\u00fcmanlar\u0131 ge\u00e7ersiz olanlardan ay\u0131rmaya \u00e7al\u0131\u015f\u0131r.<\/p>\n
Ku\u015fkusuz, mant\u0131k\u00e7\u0131 t\u00fcm arg\u00fcmanlar\u0131 tek tek test etme yoluna gitmez. Buna ne olanak vard\u0131r ne de gerek. Ge\u00e7erlik bi\u00e7ime ba\u011fl\u0131 bir \u00f6zellik oldu\u011funa g\u00f6re, somut arg\u00fcmanlar yerine bunlara \u00f6rnek olu\u015fturan \u00e7\u0131kar\u0131m kal\u0131plar\u0131na bakmak yeter. Bu kal\u0131plar say\u0131 y\u00f6n\u00fcnden s\u0131n\u0131rl\u0131, bi\u00e7im y\u00f6n\u00fcnden ise geneldir. Hem bu noktay\u0131, hem de mant\u0131ksal ge\u00e7erli\u011fin i\u00e7eri\u011fe de\u011fil, bi\u00e7ime ba\u011fl\u0131 oldu\u011funu g\u00f6stermek i\u00e7in \u00f6rnek (2)\u2019yi tekrar inceleyelim.<\/p>\n
T\u00fcm A\u2019lar B\u2019dir.
\nX bir A’d\u0131r.
\n______________
\nO halde, X bir B\u2019dir.<\/p>\n
Burada A, B ve X birer de\u011fi\u015fkendir; neleri adland\u0131rd\u0131klar\u0131 belli de\u011fildir. Ne var ki, \u00f6nc\u00fcller gene sonucu zorunlu k\u0131lmakta, \u00e7\u0131kar\u0131m ge\u00e7erli\u011fini s\u00fcrd\u00fcrmektedir. A, B, ve X simgeleri neyi temsil ederlerse etsinler, e\u011fer X bir A ise, ve A olan her \u015fey ayn\u0131 zamanda B ise, X\u2019in B olmas\u0131 ka\u00e7\u0131n\u0131lmaz bir zorunluluktur. Bu bi\u00e7im geneldir, uyguland\u0131\u011f\u0131 konu veya bilgi alan\u0131 ne olursa olsun ge\u00e7erli\u011fini s\u00fcrd\u00fcr\u00fcr.<\/p>\n
Unutmamak gerekir ki \u00f6rnek (2) bir \u00e7\u0131kar\u0131m kal\u0131b\u0131d\u0131r. Kal\u0131p ge\u00e7erli oldu\u011fundan, kal\u0131ba uyan t\u00fcm somut arg\u00fcmanlar da ge\u00e7erlidir. \u00d6rnek (1)\u2019deki gibi her somut \u00f6rnek, genel nitelikte olan \u00f6rnek (2)\u2019deki bi\u00e7imin \u00f6zel bir halini olu\u015fturur. Nitekim a\u015fa\u011f\u0131daki \u00f6rnek (1)\u2019deki arg\u00fcmandan i\u00e7erik y\u00f6n\u00fcnden farkl\u0131 olmakla birlikte \u00f6rnek (2)\u2019deki kal\u0131ba uymakta, yani ayn\u0131 bi\u00e7imi payla\u015fmaktad\u0131r.<\/p>\n
\u00d6rnek (4)<\/p>\n
T\u00fcm filler kanatl\u0131d\u0131r.
\nFino bir fildir.
\n__________________
\nO halde, fino kanatl\u0131d\u0131r.<\/p>\n
Bu \u00f6rnek, ayn\u0131 zamanda, ge\u00e7erli\u011fin i\u00e7erikten ba\u011f\u0131ms\u0131z oldu\u011funu g\u00f6stermektedir. Gerek \u00f6nc\u00fcller, gerek sonu\u00e7taki \u00f6nerme yanl\u0131\u015f oldu\u011fu halde \u00e7\u0131kar\u0131m (arg\u00fcman) ge\u00e7erlidir. \u0130\u015fte bu nedenle mant\u0131k, her konuda say\u0131s\u0131 sonsuza varan somut \u00f6rneklerle de\u011fil, bu \u00f6rneklerin \u00f6zel durum olu\u015fturdu\u011fu soyut ve genel nitelikteki bi\u00e7im veya kal\u0131plarla ilgilenir.<\/p>\n
Ku\u015fkusuz, \u00e7\u0131kar\u0131m kal\u0131plar\u0131n\u0131n t\u00fcm\u00fc ge\u00e7erli de\u011fildir. \u00d6rne\u011fin de\u011fi\u015fik bir bi\u00e7imi olan \u015fu \u00e7\u0131kar\u0131m\u0131n,<\/p>\n
\u00d6rnek (5)<\/p>\n
Ya\u011fmur ya\u011f\u0131yorsa hava bulutludur.
\n\u015eimdi ya\u011fmur ya\u011fm\u0131yor.
\n______________________________
\nO halde hava bulutlu de\u011fildir.<\/p>\n
Ge\u00e7erli olmad\u0131\u011f\u0131n\u0131 biliyoruz, \u00e7\u00fcnk\u00fc \u00e7\u0131kar\u0131m\u0131n \u00f6zel hal te\u015fkil etti\u011fi genel kal\u0131p ge\u00e7erli de\u011fildir.<\/p>\n
Mant\u0131k bize hangi \u00e7\u0131kar\u0131m kal\u0131plar\u0131n\u0131n ge\u00e7erli, hangilerinin ge\u00e7ersiz oldu\u011funu etkin ve kesinlikle ay\u0131rt etmemiz i\u00e7in, \u00e7\u0131kar\u0131m kurallar\u0131 denilen birtak\u0131m \u00f6l\u00e7\u00fctler sa\u011flar ve bu kurallar\u0131n uygulama tekniklerini \u00f6\u011fretir. \u0130\u015fte bu nedenledir ki, daha \u00f6nce, \u201cdo\u011fru d\u00fc\u015f\u00fcnme kurallar\u0131n\u0131n bilgisi\u201d diye tan\u0131mlad\u0131\u011f\u0131m\u0131z mant\u0131\u011f\u0131, \u201cge\u00e7erli \u00e7\u0131kar\u0131m veya kal\u0131plar\u0131n\u0131n bilimi\u201d diye nitelememiz belki daha do\u011fru olur. <\/p>\n
Ge\u00e7erli arg\u00fcman bi\u00e7imlerini ay\u0131rt etme ve belirleme mant\u0131kta ba\u015fl\u0131ca \u00e7al\u0131\u015fma konusudur. Ne var ki, mant\u0131ksal ge\u00e7erlik ak\u0131l-y\u00fcr\u00fctme t\u00fcrleri aras\u0131nda yaln\u0131z ded\u00fcktif \u00e7\u0131kar\u0131m t\u00fcr\u00fcnde aranabilir. Mant\u0131k\u00e7\u0131lar\u0131n \u00e7o\u011funluk ded\u00fcktif \u00e7\u0131kar\u0131m bi\u00e7imleri ile u\u011fra\u015fmalar\u0131 bundan olmal\u0131. Oysa yaln\u0131z g\u00fcnl\u00fck d\u00fc\u015f\u00fcnmede de\u011fil bilimsel arg\u00fcmanlarda da ded\u00fcktif olmayan ak\u0131l-y\u00fcr\u00fctmelere yer verildi\u011fi yads\u0131namaz. Bunlar aras\u0131nda hi\u00e7 ku\u015fkusuz \u00fczerinde en \u00e7ok durulan\u0131 ind\u00fcktif ak\u0131l-y\u00fcr\u00fctmedir. <\/p>\n
Ded\u00fcktif arg\u00fcman\u0131n ba\u015fta gelen \u00f6zelli\u011fi, \u00f6nc\u00fcllerin sonucu kesinlikle do\u011frulad\u0131\u011f\u0131 sav\u0131n\u0131 ta\u015f\u0131mas\u0131d\u0131r. Bu sav\u0131n ger\u00e7ekle\u015fmesi halinde arg\u00fcman ge\u00e7erlik kazan\u0131r; aksi halde arg\u00fcman ded\u00fcktif nitelikte olmas\u0131na kar\u015f\u0131n ge\u00e7ersiz kal\u0131r. \u00d6rne\u011fin, \u015fu arg\u00fcman,<\/p>\n
\u00d6rnek (6) <\/p>\n
Bertrand Russell ateistti.
\nT\u00fcm kom\u00fcnistler ateisttir.
\n\u00d6yle ise Bertrand Russell kom\u00fcnistti. <\/p>\n
Ded\u00fcktif t\u00fcrden olmakla birlikte mant\u0131ksal ge\u00e7erlikten yoksundur. Bir ki\u015finin, koministler gibi ataist olmas\u0131 onun kom\u00fcnist oldu\u011fu sonucunu vermez; nas\u0131l ki bir ki\u015finin, kom\u00fcnistler gibi, yemesi veya uyumas\u0131 onu kom\u00fcnist saymam\u0131z\u0131 gerektirmez. Nitekim arg\u00fcmanda \u00f6nc\u00fcller do\u011fru oldu\u011fu halde sonu\u00e7 yanl\u0131\u015ft\u0131r.<\/p>\n
Buna kar\u015f\u0131l\u0131k yukar\u0131daki \u00f6rne\u011fimizi (6) a\u015fa\u011f\u0131daki gibi de\u011fi\u015ftirdi\u011fimizde,<\/p>\n
\u00d6rnek (7)<\/p>\n
Bertrand Russell ataistti.
\nT\u00fcm ataistler kom\u00fcnisttir.
\n\u00d6yle ise Bertrand Russel kom\u00fcnistti.<\/p>\n
Ded\u00fcktif t\u00fcrden ge\u00e7erli bir arg\u00fcman elde etmekteyiz. Ger\u00e7ekten bu \u00f6rnekte \u00f6nc\u00fclleri do\u011fru, sonucu yanl\u0131\u015f saymak \u00e7eli\u015fkiye d\u00fc\u015fmek olur. Bir \u015feyin A gibi bir \u00f6zelli\u011fi varsa, A \u00f6zelli\u011fi olan her \u015feyin ayn\u0131 zamanda B gibi bir \u00f6zelli\u011fi varsa, o \u015feyin B \u00f6zelli\u011fi olmas\u0131 ka\u00e7\u0131n\u0131lmazd\u0131r. Ancak bir \u015fey ba\u015fka birtak\u0131m \u015feylerle belli bir \u00f6zelli\u011fi payla\u015f\u0131yorsa, bundan o \u015feyin di\u011fer \u015feylere ait ba\u015fka bir \u00f6zelli\u011fi de payla\u015ft\u0131\u011f\u0131 sonucu \u00e7\u0131kmaz.<\/p>\n
Demek oluyor ki, bir arg\u00fcman\u0131n ded\u00fcktif olmas\u0131 onun mutlaka ge\u00e7erli oldu\u011fu anlam\u0131na gelmez. Ayn\u0131 \u015fekilde, bir arg\u00fcman\u0131n ge\u00e7erli olmas\u0131 onun sonucunu ispatlad\u0131\u011f\u0131 demek de de\u011fildir. Sonucun do\u011fru olarak ispatlanmas\u0131 hem arg\u00fcman\u0131n ge\u00e7erli olmas\u0131n\u0131 hem de \u00f6nc\u00fcllerin do\u011fru olmas\u0131n\u0131 gerektirir. Nitekim \u00f6rnek (7)\u2019deki arg\u00fcman ge\u00e7erli olmas\u0131na kar\u015f\u0131n, sonucunu ispatlayamam\u0131\u015ft\u0131r; zira \u00f6nc\u00fcllerden biri (\u201cT\u00fcm ateistler kom\u00fcnisttir\u201d) yanl\u0131\u015ft\u0131r. <\/p>\n
Bir arg\u00fcman\u0131n ded\u00fcktif olmas\u0131 ge\u00e7erli olmas\u0131 i\u00e7in gerekli ama yeterli de\u011fildir. Ded\u00fcktif oldu\u011fu halde ge\u00e7erli olmayan arg\u00fcman vard\u0131r; buna bir \u00f6rnek verdik. Ancak ge\u00e7erli oldu\u011fu halde ded\u00fcktif olmayan bir arg\u00fcman yoktur; bir arg\u00fcman ge\u00e7erli ise mutlaka ded\u00fcktiftir. Bu demektir ki, ge\u00e7erli arg\u00fcmanlar ded\u00fcktif \u00e7\u0131kar\u0131mlar\u0131n bir alt grubunu olu\u015fturur.<\/p>\n
Ne var ki, ak\u0131l y\u00fcr\u00fctmelerimizin t\u00fcm\u00fc ded\u00fcktif t\u00fcrden de\u011fildir ve bunlar\u0131n mant\u0131k ve matematik gibi ispata y\u00f6nelik alanlar d\u0131\u015f\u0131ndaki etkinli\u011fi g\u00f6rmezlikten gelinemez. \u015eu \u00f6rnekleri inceleyelim.<\/p>\n
Yerler \u0131slak, o halde ya\u011fmur ya\u011fm\u0131\u015f olmal\u0131.
\nAli \u00e7ok \u015fi\u015fmanlayacak, \u00e7\u00fcnk\u00fc durmadan yiyor.<\/p>\n
Bunlar\u0131n hepsi ded\u00fcktif olmayan t\u00fcrden ak\u0131l-y\u00fcr\u00fctmeler. Birincisinde bir g\u00f6zlemimiz (yerlerin \u0131slakl\u0131\u011f\u0131) bizi g\u00f6zlem konusu olmayan ba\u015fka bir olguya g\u00f6t\u00fcrmekte. Ya\u011fmurun ya\u011fm\u0131\u015f oldu\u011funu d\u00fc\u015f\u00fcnmekle yerlerin \u0131slakl\u0131\u011f\u0131n\u0131 a\u00e7\u0131klam\u0131\u015f oluyoruz. Ne var ki bu a\u00e7\u0131klama zorunlu de\u011fildir; yerler ba\u015fka t\u00fcrl\u00fc de \u0131slat\u0131lm\u0131\u015f olabilir. O halde yerlerin \u0131slakl\u0131\u011f\u0131, ya\u011fmurun ya\u011fm\u0131\u015f olmas\u0131n\u0131 d\u00fc\u015f\u00fcnmemiz i\u00e7in bir neden, hem de \u00e7o\u011fu kez do\u011fru bir neden olmakla birlikte, yeter bir neden de\u011fildir. Ba\u015fka bir deyi\u015fle yerlerin \u0131slak olmas\u0131, ya\u011fmurun ya\u011fm\u0131\u015f oldu\u011funa y\u00fcksek bir olas\u0131l\u0131k sa\u011flamakta, ama onu zorunlu k\u0131lmamaktad\u0131r. Nitekim d\u00fczg\u00fcn arg\u00fcman bi\u00e7iminde s\u00f6z konusu ak\u0131l y\u00fcr\u00fctmenin ge\u00e7erli olmad\u0131\u011f\u0131 g\u00f6r\u00fclmektedir.<\/p>\n
\u00d6rnek ( 8 )<\/p>\n
Yerler \u0131slanm\u0131\u015f
\n_________________
\nO halde, ya\u011fmur ya\u011fm\u0131\u015f olmal\u0131.<\/p>\n
\u00d6nc\u00fclden sonuca ge\u00e7i\u015fte ge\u00e7mi\u015f ya\u015fant\u0131m\u0131z bize g\u00fc\u00e7l\u00fc dayanak vermekle birlikte hi\u00e7bir mant\u0131ksal zorunluluk yoktur. Arg\u00fcman\u0131n ge\u00e7erli olmas\u0131 i\u00e7in, genelleme niteli\u011finde \u015f\u00f6yle bir \u00f6nc\u00fcle daha dayanmam\u0131z gerekir. Yerler \u0131slaksa, ya\u011fmur ya\u011fm\u0131\u015f olmal\u0131. Ancak bu t\u00fcmcenin \u00f6nc\u00fcle eklenmesi ile arg\u00fcman niteli\u011fini de\u011fi\u015ftirmekte, ded\u00fcktif bir kimlik kazanmaktad\u0131r. <\/p>\n
\u0130kinci \u00f6rnek birincisinden pek farkl\u0131 de\u011fildir. \u015eu kadar ki, burada ak\u0131l y\u00fcr\u00fctmemiz bir g\u00f6zlemimizi, g\u00f6zlem d\u0131\u015f\u0131 bir olguya giderek a\u00e7\u0131klamaya de\u011fil, bir g\u00f6zleme dayanarak hen\u00fcz olmam\u0131\u015f bir olguyu beklemeye y\u00f6nelik. Ge\u00e7mi\u015f ya\u015fant\u0131 veya g\u00f6zlemlerimizden, \u00e7ok yemekle \u015fi\u015fmanlama aras\u0131nda bir ili\u015fkinin var oldu\u011funu biliyoruz. \u015ei\u015fman bir kimse bize \u201ciyi beslenmi\u015f\u201d oldu\u011funu d\u00fc\u015f\u00fcnd\u00fcrebilece\u011fi gibi, \u00e7ok yiyen bir kimsenin \u015fi\u015fmanlayaca\u011f\u0131n\u0131 da d\u00fc\u015f\u00fcnebiliriz. Ancak bu ili\u015fki gene olas\u0131l\u0131ktan \u00f6te bir kesinlik sa\u011flamamaktad\u0131r. Ali\u2019nin \u00e7ok yemesine bakarak onun \u015fi\u015fmanlayaca\u011f\u0131n\u0131 bekleyebiliriz. Ancak \u00e7ok yeme, \u015fi\u015fmanlama i\u00e7in yeter bir neden olmad\u0131\u011f\u0131ndan, bekledi\u011fimiz sonu\u00e7 zorunlu de\u011fil, iki olgu aras\u0131ndaki ili\u015fkinin sa\u011flaml\u0131k derecesine g\u00f6re olas\u0131d\u0131r. Arg\u00fcman burada da ge\u00e7erli de\u011fildir:<\/p>\n
\u00d6rnek (9)<\/p>\n
Ali durmadan yiyor.
\n________________
\nO halde, Ali \u015fi\u015fmanlayacak.<\/p>\n
Ak\u0131l y\u00fcr\u00fctmeler \u00f6nermeler aras\u0131 bir ili\u015fki olup, bir ak\u0131l y\u00fcr\u00fctme i\u00e7in, elimizde en az biri kan\u0131tlayan ve di\u011feri kan\u0131tlanan konumunda iki \u00f6nerme bulunmas\u0131 gerekmekte ve ded\u00fcksiyon, \u00f6nermeler aras\u0131ndaki bir kan\u0131tlama ili\u015fkisi olarak kar\u015f\u0131m\u0131za \u00e7\u0131kmaktad\u0131r.<\/p>\n
Ama acaba birden fazla \u00f6nermeyi i\u00e7eren her \u00f6nerme grubu i\u00e7inde bir kan\u0131tlama ili\u015fkisi var m\u0131d\u0131r? Veya ba\u015fka t\u00fcrl\u00fc sorarsak: Herhangi iki \u00f6nerme aras\u0131nda birini kan\u0131tlayan di\u011ferini kan\u0131tlanan olarak ele al\u0131p bir ak\u0131l y\u00fcr\u00fctme ili\u015fkisi kurmak m\u00fcmk\u00fcn m\u00fcd\u00fcr?<\/p>\n
Hemen yan\u0131tlayal\u0131m: \u00d6nermeler aras\u0131nda her zaman ve her durumda bir ak\u0131l y\u00fcr\u00fctme ili\u015fkisi yoktur. \u00d6rne\u011fin \u201cBal tatl\u0131d\u0131r\u201d ile \u201cTur\u015fu ek\u015fidir\u201d \u00f6nermeleri aras\u0131nda bir kan\u0131tlayan-kan\u0131tlanan ili\u015fkisi yoktur. Bunlar birbirlerinden ba\u011f\u0131ms\u0131z \u00f6nermelerdir. Her iki \u00f6nerme de do\u011fru \u00f6nermelerdir; ama birinin do\u011frulu\u011fu di\u011ferinin do\u011frulu\u011funun bir kan\u0131t\u0131 veya gerek\u00e7esi olmamaktad\u0131r. Dolay\u0131s\u0131yla bu iki \u00f6nerme aras\u0131nda bir ak\u0131l y\u00fcr\u00fctme ili\u015fkisi yoktur. <\/p>\n
Demek ki, t\u00fcm \u00f6nermeler aras\u0131nda bir ak\u0131l y\u00fcr\u00fctme ili\u015fkisi olmas\u0131 gerekmez. Ak\u0131l y\u00fcr\u00fctme, aralar\u0131nda bir kan\u0131tlayan-kan\u0131tlanan ili\u015fkisi kurabilece\u011fimiz \u00f6nermeler i\u00e7in s\u00f6z konusudur. \u00d6rne\u011fin \u201cB\u00fct\u00fcn insanlar \u00f6l\u00fcml\u00fcd\u00fcr\u201d \u00f6nermesi ile \u201cSokrates \u00f6l\u00fcml\u00fcd\u00fcr\u201d \u00f6nermesi aras\u0131nda bir kan\u0131tlayan-kan\u0131tlanan ili\u015fkisi kurabiliyoruz ve Sokrates\u2019in \u00f6l\u00fcml\u00fc olmas\u0131n\u0131n kan\u0131t\u0131n\u0131, b\u00fct\u00fcn insanlar\u0131n \u00f6l\u00fcml\u00fc olmas\u0131 olarak g\u00f6sterebiliyoruz. Burada kan\u0131tlayan-kan\u0131tlanan ili\u015fkisini nas\u0131l kurdu\u011fumuzu a\u00e7\u0131klayabiliriz: Her iki \u00f6nermede ortak olan terimler (\u201cinsan-\u00f6l\u00fcml\u00fc\u201d) vard\u0131r. Bu ortak terimlerden \u201cinsan\u201d terimi, birinci \u00f6nermede bir \u00f6zelli\u011fine g\u00f6re i\u00e7lemsel yoldan tan\u0131mlanm\u0131\u015ft\u0131r; yani t\u00fcm insanlar\u0131n \u00f6l\u00fcml\u00fc oldu\u011fu bilinmektedir ve dolay\u0131s\u0131yla bunun tek bir insan (Sokrates) i\u00e7in de ge\u00e7erli olaca\u011f\u0131 a\u00e7\u0131kt\u0131r. Burada kan\u0131tlamay\u0131, i\u00e7lem-kaplam, cins-t\u00fcr, s\u0131n\u0131f-\u00fcye (fert, birey) ili\u015fkisi temelinde ve her iki \u00f6nermedeki ortak terimlere dayanarak kurmu\u015f oldu\u011fumuz da a\u00e7\u0131k\u00e7a g\u00f6r\u00fclmektedir.<\/p>\n
K\u0131sacas\u0131, kan\u0131tlama (arg\u00fcmantasyon) dedi\u011fimiz mant\u0131ksal i\u015flem, bir cin-t\u00fcr, s\u0131n\u0131f-\u00fcye ili\u015fkisine sokabildi\u011fimiz kavramlar (terimler) ve bu kavramlar\u0131 i\u00e7eren \u00f6nermeler i\u00e7in s\u00f6z konusudur. O halde ded\u00fcktif mant\u0131\u011fa ait konular kavramlar mant\u0131\u011f\u0131ndan hareketle anla\u015f\u0131labilir ve ded\u00fcktif mant\u0131k, temelini kavramlar mant\u0131\u011f\u0131nda bulur. B\u00f6yle g\u00f6r\u00fcld\u00fc\u011f\u00fcnde, ded\u00fcktif mant\u0131\u011f\u0131n (\u00f6zellikle Aristotales\u2019de) bir s\u0131n\u0131rlar mant\u0131\u011f\u0131na dayand\u0131\u011f\u0131n\u0131 saptayabiliriz. <\/p>\n
\u00c7\u0131kar\u0131m \u00c7e\u015fitleri :<\/p>\n
\u00c7\u0131kar\u0131mlar (ded\u00fcksiyonlar) iki ana \u00e7e\u015fide ayr\u0131l\u0131rlar:<\/p>\n
Do\u011frudan \u00e7\u0131kar\u0131mlar
\nDolayl\u0131 \u00e7\u0131kar\u0131mlar<\/p>\n
Do\u011frudan \u00e7\u0131kar\u0131mlar; tek bir \u00f6nc\u00fclden sonuca ge\u00e7ilen, yani biri \u00f6nc\u00fcl di\u011feri sonu\u00e7 olmak \u00fczere iki \u00f6nermeden olu\u015fan \u00e7\u0131kar\u0131mlard\u0131r. Zihnimizin birinci \u00f6nermeden, arada ba\u015fka bir \u00f6nerme kullanmaks\u0131z\u0131n do\u011frudan do\u011fruya, sonu\u00e7 \u00e7\u0131karmak suretiyle yapt\u0131\u011f\u0131 ak\u0131l y\u00fcr\u00fctme \u015feklidir. \u00d6rne\u011fin “Her insan canl\u0131d\u0131r” \u00f6nermesi bilinen bir ger\u00e7ekse, zihminiz, hi\u00e7bir arac\u0131 \u00f6nerme kullanmaks\u0131z\u0131n “Baz\u0131 canl\u0131lar, insand\u0131r” sonucunu \u00e7\u0131karabilir. Bu do\u011frudan t\u00fcmdengelim \u015feklidir. <\/p>\n
Bunlarda kendi i\u00e7lerinde, a) kar\u015f\u0131olum \u00e7\u0131kar\u0131mlar\u0131, b)e\u015fde\u011ferlik \u00e7\u0131kar\u0131mlar\u0131 olmak \u00fczere iki alt \u00e7e\u015fide ayr\u0131l\u0131rlar. Kar\u015f\u0131olum \u00e7\u0131kar\u0131mlar\u0131, a) kar\u015f\u0131tl\u0131k \u00e7\u0131kar\u0131mlar\u0131, b) altl\u0131k \u00e7\u0131kar\u0131mlar\u0131, c) \u00e7eli\u015fki \u00e7\u0131kar\u0131mlar\u0131 \u00e7e\u015fitlerini kapsarlar. Bunun gibi e\u015fde\u011ferlik \u00e7\u0131kar\u0131mlar\u0131, a) evirme, b) \u00e7evirme, c) devirme \u00e7e\u015fitlerini i\u00e7ine al\u0131r.<\/p>\n
Dolayl\u0131 \u00e7\u0131kar\u0131mlar; zihnimizin, birinci \u00f6nermeden sonuca ge\u00e7erken, arada ba\u015fka \u00f6nermelerden yararlanmak suretiyle yapm\u0131\u015f oldu\u011fu ak\u0131l y\u00fcr\u00fctme \u015feklidir, en az iki \u00f6nc\u00fcl ve bir sonu\u00e7 \u00f6nermesinden kurulu yani en az \u00fc\u00e7 \u00f6nermeyi i\u00e7eren \u00e7\u0131kar\u0131mlard\u0131r. \u00d6rne\u011fin: “\u0130nsanlar \u00f6l\u00fcml\u00fcd\u00fcr, Sokrates insand\u0131r. O halde Sokrates’de \u00f6l\u00fcml\u00fcd\u00fcr. <\/p>\n
Klasik mant\u0131kta en \u00e7ok verilen \u00e7\u0131kar\u0131mlard\u0131r. Bu \u00e7\u0131kar\u0131m \u00e7e\u015fidine ayr\u0131ca ve daha yayg\u0131n adlar\u0131yla tas\u0131m, k\u0131yas, sillogizm adlar\u0131 da verilir. Dolayl\u0131 \u00e7\u0131kar\u0131mlar kendi i\u00e7inde iki ana \u00e7e\u015fide ayr\u0131l\u0131rlar: a) kategorik tas\u0131m, b) kategorik olmayan tas\u0131m. Kategorik tas\u0131m, \u00f6nc\u00fclleri ve sonucu yani t\u00fcm \u00f6nermeleri basit (kategorik) \u00f6nermelerden olu\u015fan tas\u0131md\u0131r. Kategorik olmayan tas\u0131m ise, a) hipotetik tas\u0131m, b) disjunktif tas\u0131m, c) ikilem (dilemma) olarak kendi i\u00e7inde \u00fc\u00e7 alt \u00e7e\u015fide ayr\u0131l\u0131r.<\/p>\n
Sonu\u00e7: <\/p>\n
G\u00fcn\u00fcm\u00fczde hala bilimsel d\u00fc\u015f\u00fcncede rol oynayan t\u00fcmdengelim, t\u00fcmel (genel) bir \u00f6nermeden tikel (\u00f6zel) \u00f6nerme \u00e7\u0131karma eylemidir. \u00d6rne\u011fin, fizikte genel \u00e7ekim yasas\u0131n\u0131 biliyorsan\u0131z, Newton\u2019un ba\u015f\u0131na d\u00fc\u015ft\u00fc\u011f\u00fc rivayet edilen elman\u0131n yapt\u0131\u011f\u0131 etkiyi hesaplayabilirsiniz. Bu, \u00f6nemsiz g\u00f6r\u00fcn\u00fcyorsa, uzaya f\u0131rlataca\u011f\u0131n\u0131z bir ileti\u015fim uydusunun istenen y\u00f6r\u00fcngeye oturmas\u0131 i\u00e7in, nereden hangi h\u0131zla, hangi e\u011fimle f\u0131rlat\u0131lmas\u0131 gerekti\u011fini de hesaplayabilirsiniz. Bu \u00f6rnekte s\u00f6ylendi\u011fi gibi, t\u00fcmel bir \u00f6nermeden tikel \u00f6nerme \u00e7\u0131kar\u0131l\u0131\u015f\u0131n\u0131 sa\u011flayan yordama usavurma denmektedir. De\u011fi\u015fik kaynaklarda buna, t\u00fcmdengelim, ak\u0131l y\u00fcr\u00fctme, tas\u0131m (k\u0131yas), ded\u00fcksiyon, \u00e7\u0131kar\u0131m adlar\u0131 verilmektedir. Mant\u0131k usavurma kurallar\u0131n\u0131 konu edinen bilim dal\u0131d\u0131r. Ba\u015fka bir deyi\u015fle mant\u0131k t\u00fcmdengelim y\u00f6ntemlerini inceler. Bu \u00f6devde de t\u00fcmdengelim kavram\u0131 a\u00e7\u0131klanmaya \u00e7al\u0131\u015f\u0131lm\u0131\u015ft\u0131r.<\/p>\n","protected":false},"excerpt":{"rendered":"
Tarihsel Geli\u015fim: \u201cT\u00fcmdengelim\u201d y\u00f6ntemi mant\u0131kta, bir yada daha fazla \u00f6nc\u00fclden zorunlu olarak sonucun \u00e7\u0131kar\u0131lmas\u0131d\u0131r ve t\u00fcmelle tikel (genelle \u00f6zel) aras\u0131nda s\u0131k\u0131 bir ili\u015fki g\u00f6ren ve bu ili\u015fkiyi en do\u011fru olarak ortaya koyman\u0131n yollar\u0131n\u0131 ara\u015ft\u0131ran Aristotales\u2019in bulu\u015fudur. Aristotales, antik\u00e7a\u011f Yunan d\u00fc\u015f\u00fcncesinde \u00e7a\u011fda\u015f anlam\u0131yla ilk bilgindir. Kendisinden \u00f6nce b\u00fct\u00fcn bilgileri toplam\u0131\u015f, i\u00e7 i\u00e7e ge\u00e7mi\u015f olanlar\u0131 birbirinden ay\u0131rm\u0131\u015f, …<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[1403,1406],"tags":[3029,3028,3030],"class_list":["post-1017","post","type-post","status-publish","format-standard","hentry","category-odevler","category-sosyal-bilgiler-odevleri","tag-aristotales","tag-tumdengelim","tag-tumevarim"],"_links":{"self":[{"href":"https:\/\/www.islamidavet.com\/kutuphane\/wp-json\/wp\/v2\/posts\/1017","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.islamidavet.com\/kutuphane\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.islamidavet.com\/kutuphane\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.islamidavet.com\/kutuphane\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.islamidavet.com\/kutuphane\/wp-json\/wp\/v2\/comments?post=1017"}],"version-history":[{"count":0,"href":"https:\/\/www.islamidavet.com\/kutuphane\/wp-json\/wp\/v2\/posts\/1017\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.islamidavet.com\/kutuphane\/wp-json\/wp\/v2\/media?parent=1017"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.islamidavet.com\/kutuphane\/wp-json\/wp\/v2\/categories?post=1017"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.islamidavet.com\/kutuphane\/wp-json\/wp\/v2\/tags?post=1017"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}