
abhedyatha

ganithashaasthram, yukthishaasthram, ganithashaasthram ennivayude thathwachintha ennivayil, svayam paraamarsikkunna nirvachanam abhilashaneeyamaanu. ekadesham paranjaal, oru nirvachanam nirvachikkappedunna settine (paraamarshikkukayo alakkukayo cheyyuka) allengil (kooduthal saadhaaranayaayi) nirvachikkappedunna kaaryam adangiyirikkunna mattoru settine (alakkukayo cheyyuka) abhyarthikkukayaanenkil athu abhikaamyamaanu. pravachanamo anumaanaparamo ennathinte ardham enthaanennathinu pothuvaayi amgeekarikkappetta krithyamaaya nirvachanamilla. rachayithakkal vyathyasthavum ennaal anubandhavumaaya nirvachanangal nalkiyittundu.
impredisittivittiyu vipareethamaanu predictivity, ithu pradhaanamaayum sthareekritha (allengil ramified) sidhaanthangal nirmmikkunnu, avide thaazhnna thalangalile alavu chila puthiya tharam veriyabilukalil kalaashikkunnu, ithu variable shreniyile thaazhnna tharangalil ninnu vyathyasthamaan. oru prototypic udaaharanam avabodhajanyamaaya tharam sidhaanthamaanu, ithu impredikattivitti upekshikkunnathinayi ramification nilanirthunnu.
rassalinte vairudhyam oru abhilashaneeyamaaya nirmmaanatthinte prashasthamaaya udaaharanamaanu-athaayath svayam ulkkollaatha ellah settukaludeyum koottam. atharamoru koottam nilanilkkaan kazhiyilla ennathaanu vairudhyam athu nilanilkkumo ennu chodichaal, athil svayam adangiyirikkunno illayo enna chodyam chodikkaam-angane cheythaal nirvachanam anusarichu athu paadilla, illengil nirvachanam anusarichu athu cheyyanam.
oru koottatthinte ettavum valia thaazhnna paridikkum oru abhilashaneeyamaaya nirvachanamunda ellah gadakangalkkum, ellah gadakangalekkaalum kuravo thulyamo aanenkil, ellah gadakangalekkaalum kuravo thulyamo aanenkil maathram. eee nirvachanam settinu mukaliloode alakkunnu (samshayaaspadamaaya kramatthe aashrayich ananthamaayirikkaam) athinte amgangal thaazhathe paridhikalaan, avayilonnu jii. ell. bii thanne aanu. athinaal pravachanavaadam eee nirvachanam nirsikkum.
charithram.
pravachanam", "anumaanathmakam" ennee padangal avatharippichathu, ennirunnaalum athinusesham ardham alppam maari. 
solaman fefferman pravachanathekkurichulla oru charitraparamaaya avalokanam nalkunnu, ithu nilavile mikacha gaveshana prasnangalumaayi bandhippikkunnu.
niyamaanusrithamaaya settu savisheshathakalile aavasyakathayaayi vairudhyangalude pashchaathalatthil henry poincare (1905-6,1908) bertrand russel vishachakra thathwam nirddeshichu. aavasyakatha niravettaattha settukale "inpredicative" ennu vilikkunnu.
aadyathe aadhunika vairudhyam siser burali-forty 1897-leeii "transfinite nambarukalekkurichulla oru chodyam" ennathumaayi prathyakshappedukayum athu burali-forty vairudhyam ennariyappedukayum cheythu. kaantor thante (kaantorinte) "nishkalanka" settu sidhaanthathil ithe vairudhyam kandethiyirunnuvennum ithu kaantorinte vairudhyam ennariyappedunnathaayum kaanapedunnu. 1901 juunil frejinte ganithashaasthra yukthiyekkurichulla grandhamaaya 1879 leeii "begifscrift" vaayikkunnathiloodeyaanu prashnathekkurichulla rassalinte avabodham uthbhavichath; frejile kuttakaramaya vaachakam inipparayunnavayaanu
mattoru vidhathil paranjaal, function variable invariyant bhagavumaanu. appol enthukondu moolyam svayam maattisthaapikkaruth? russell udan thanne freejinu oru kathu ezhuthi
prashnam amgeekarichukondu freej udan thanne russellinu ezhuthi
eee prashnam iruvarkkum prathikoolamaaya vyakthiparamaaya prathyaaghaathangal srishtichappol (iruvarkkum printarukalil ulppeduthenda jolikal undaayirunnu), "eee vairudhyam yukthivaadikalude lokathe ilakki marichuvennum aaa kolaahalangal innum anubhavappedunnundennum vaan hygenort nireekshikkunnu. ... settinteyum moolakathinteyum nagnamaaya ashayangal upayogikkunna rassalinte vairudhyam yukthiyude mekhalayil chathuraakrithiyil varunnu. ganithashaasthrathinte thathwangal" (1903) enna pusthakathilaanu russell aadyamaayi eee vairudhyam prasidheekarichathu, athu avide valare vishadamaayi charcha cheyyappedunnu...". aarr varshathe thettaaya thudakkangalkk sesham, russell oduvil 1908 leeii thante "reducibility enna sidhaantham" munnottuvachukondu thante tharangalude sidhaanthathiloode eee vishayathin utharam nalki. eathu function addeham "predicative" function ennu vilikkunnathumaayi sahavarthikkunnundenn athu parayunnu prathyaksha veriyabilukalude tharangal aargyumentukalude tharangalekkaal uyarnnathallaatha oru function. ennaal eee "sidhaanthathinu" ellah konukalil ninnum ethirppu nerittu.
avishwasaneeyamaayi nirvachikkapetta ganithashaasthra vasthukkale nirasikkunnath (classicalaayi manassilaakkiyathupole swaabhaavika samkhyakale sweekarikkumbol) henry poinkar herman veyilum thante "daas kondinyoom" enna kruthiyil vaadicha predicativism ennariyappedunna ganithashaasthra thathwashaasthrathile sthaanathekku nayikkunnu. onno athiladhikamo adisthaana settukal ananthamaakumbol maathrame inpredicative nirvachanangal prashnakaramaakoo ennu poincare weylum vaadichu.
1908-ll ernst sermelo thante "oru nalla oordaringinte saadhyathayude oru puthiya thelivu" oru muzhuvan vibhaagavum avatharippikkunnu ". "poyinkeyarinethire addeham vaadicha" "nonpredicative nirvachanathekkurichulla ethirppu (1906, peju. 307) [aaraan parayunnath] oru nirvachanam 'pravachana' vum, nirvachikkapetta ashayathe aashrayichirikkunna ellah vasthukkalum, athaayath, eathu vidhathilum athu nirnnayikkaan kazhiyumennu, athu "ozhivaakkukayaanenkil" maathram yukthisahamaayi sveekaaryavumaanu. addeham anumaanathmaka nirvachanangalude rund udaaharanagal nalkunnu-(i) didikind shringalakalude ashayam, (ii) vishakalanathil munbu nirvachicha "poortthiyaakkiya" samkhyakalude koottatthinte paramavadhi allengil ettavum kuravu kooduthal nigamanangalkkayi upayogikkunnu. udaaharanathinu, ariyappedunna kaachi proofil ithu sambhavikkunnu...". addeham thante vibhaagam avasaanippikkunnath thaazhepparayunna nireekshanathodeyaanu "oru nirvachanam nirvachikkappettathin thulyamaaya aashayangale nannayi aashrayikkaam; theerchayaayum, ellah nirvachanangalilum" definions "" defindavum "thulyamaaya aashayangalaanu, koodaathe pooyinkeyarinte aavasyam karsanamaayi paalikkunnath ellah nirvachanangaleyum asaadyamaakkum, athinaal ellah shaasthravum asaadyamaanu".
munbu nirvachicha "poortthiyaakkiya" akkangalude koottatthinte ettavum kuranjathum koodiyathum enna sermeloyude udaaharanam clean <aii. dii. 1> ll veendum prathyakshappedunnu, avide clean impredicative nirvachanangalekkurichulla charchayil ettavum kuranja upper boundinte udaaharanam upayogikkunnu; clean eee prashnam pariharikilla. adutha khandikakalil addeham thante 1918 leeii "daas kondinam" ("dhii kandiniyam") enna kruthiyil abhilashaneeyamaaya nirvachanangal illaathaakkaanulla veylinte sramathekkurichum "oru uyarnna paridhiyulla shoonyamallaatha oru koottam yadhaartha samkhyakalkku ettavum kuranja upper boundu (cf) undenna sidhaantham nilanirthunnathile paraajayathekkurichum charcha cheiyunnu. 1919-lum).
inpredicative" nirvachanangal nirupadravakaramaanennu ramse vaadichu udaaharanathinu, "muriyile ettavum uyaram koodiya vyakthi" enna nirvachanam inpredicative aanu, kaaranam ithu oru gadakamaaya oru koottam kaaryangale aasrayichirikkunnu, athaayath muriyile ellah vyakthikaludeyum koottam. ganithashaasthrathe sambandhichidatholam, oru anumaanathmaka nirvachanatthinte oru udaaharanam oru koottatthile ettavum cheria samkhyayaanu, ithu aupachaarikamaayi nirvachikkappedunnu ellah gadakangalkkum, kuravo thulyamo aanenkil maathram, ullilaanengil.
burgus (2005) freejinte lojik, peeno ganithashaasthram, second oordar ganithashaasthram, svayamsidhamaaya settu sidhaantham ennivayude pashchaathalatthil pravachanaparavum abhilashaneeyavumaaya sidhaanthangal charcha cheiyunnu.

