
prakaar siddhant kaa itihas

prakaar siddhant shuru mein vibhinn prakaar key aupchaarik tark aur punarlekhan pranaliyon mein virodhabhason seey bachane key liye banaaya gayaa thaa. baad mein, prakaar siddhant ney aupchaarik pranaliyon key ack varg koo sandarbhit kiya, jinamen seey kuchh sabhi ganit key liye ack neenv key roop mein saral sett siddhant key vikalp key roop mein kaam curr sakate hain.
yeh aaj key pramaan sahayakon key liye "princia mathematesa" key baad seey aupchaarik ganit seey judaa huaa haye.
1900-1927.
russell key prakaron key siddhant kii utpatti.
gottlob fraze (1902) koo likhe ack patra mein, bertrand russell ney fraze key begrifscrift mein virodhabhas kii apani khoj kii ghoshana kii. freeze ney turant pratikriya dee, samasya koo sweekaar kiya aur "staron" kii takniki charcha mein samadhan kaa prastaav rakhaa. fraze koo uddhrit karane key liyeh
sanyog seey, mujhe aisaa lagata haye kii "ack vidheya swayam hii purvanirdhaarit haye" abhivyakti sateek naheen haye. ack vidheya ack niyam key roop mein ack pratham-stariya falan haye, aur iss falan key liye tark key roop mein ack vastu kii aavashyakta hoti haye aur swayam koo tark (vishay) key roop mein naheen hoe sakata haye. isaliye main yeh kahana pasand karunga kii "ack avadharana apane swayam key vistaar seey purvanirdhaarit haye.
vaha yeh dikhaane key baare mein jaataa haye kii yeh kaise kaam curr sakata haye lekin aisaa lagata haye kii isase peechhe hutt jaataa haye. russell key virodhabhas key roop mein jaanaa jaane vaale key parinamswarup, freeze aur russell donon koo printer parr unake karyon mein jaldi seey sanshodhan karna padaa. ack parishisht bee mein joe russell ney apane "ganit key siddhanton" (1903) parr dhyaan diyaa, vaha apane "sambhaavit" prakaron key siddhant koo paataa haye. yeh mamla lagbhag paanch varshon taka russell koo pareshan kartaa rhaa.
willard quine prakaron key siddhant aur prakaron key "vistrit" siddhant kii utpatti kaa ack aitihaasik saransh prastut karate hainh prakaron key siddhant (1905) koo chhodane parr vichaar karane key baad, russell ney teen siddhanton kaa prastaav rakhaah
quine kaa maanana haye kii russell dwara "spasht charr" kii dhaarana kii shuruat kaa nimnalikhit parinam thaah
sabhi' aur 'kissy bhee' key beach kaa antarah 'sabhi' koo saarvbhaumik matratmakta key baadhya ('spasht') charr dwara vyakt kiya jaataa haye, joe ack prakaar parr hotaa haye, aur 'koee bhee' koo mukt ('vaastavik') charr dwara vyakt kiya jaataa haye joe kissy bhee prakaar kii parwah kiye binaa kissy bhee anirdisht cheez koo yojnabaddh roop seey sandarbhit kartaa haye.
quine "baadhya charr" kii iss dhaarana koo "prakaron key siddhant key ack nishchit pahalu seey alag arthaheen" key roop mein khariz curr detaa haye.
1908 kaa "shrenibaddh" prakaar kaa siddhant.
quine "shrenibaddh" siddhant koo iss prakaar samajhaate hainh "ise isaliye kahaa gayaa haye kyonki ack kaary kaa prakaar isake tarkon key prakaar aur isamen nihit spasht charr key prakaar (yaa isaki abhivyakti mein) donon parr nirbhar kartaa haye, yadi yeye tarkon key prakaron seey adhik hain. stephen clean ney apane 1952 key "metamathematics key parichay" mein prakaron key "vistrit" siddhant kaa varnan iss tarah seey kiya haih
cumm karane kii kshamata aur "matricks" kii dhaarana kaa swayamsiddh siddhant.
lekin kyonki parivisht siddhant kii shartein (quine koo uddhrit karane key liye) "bhaari" saabit hongi, russell ney apane 1908 key "ganitiya tark key roop mein prakaron key siddhant" mein bhee apane "hraas key swayamsiddh" kaa prastaav rakhaa. 1910 taka whitehead aur russell ney apane "princia mathematesa" mein iss swayamsiddh koo "matricks" kii dhaarana key saath aur badhaa diyaa-ack kaary kaa poori tarah seey vistaratmak vinirdesh. isake matricks seey ack kaary "saamaanyikaran" kii prakriya dwara praapt kiya jaa sakata haye aur isake vipareet, i.ee. donon prakriyaaen prativarti hain-(i) ack matricks seey ack kaary mein saamaanyikaran (spasht charr kaa upayog karke) aur (ii) spasht charr key liye tarkon key pathyakram-moolya pratisthaapan dwara prakaar kii kamee kii vipareet prakriya. iss vidhi seey abhedyata seey bachaa jaa sakata haye.
satya taalikaaen.
1921 mein, emil post "satya karyon" aur unaki satya taalikaon kaa ack siddhant vikasit karega, joe spasht banaam vaastavik charr kii dhaarana koo pratisthaapit kartaa haye. unake "parichay" (1921) seh "jabaki poorna siddhant [whitehead aur russell (1910,1912,1913)] key liye isake prastaavon key vaastavik aur spasht charr key uchchaaran kii aavashyakta hoti haye, joe vibhinn prakaar key vyaktiyon aur prastavatmak karyon donon kaa pratinidhitva karate hain, aur parinamswarup prakaron key bojhil siddhant kii aavashyakta hoti haye, yeh upa-siddhant kewal vaastavik charr kaa upayog kartaa haye, aur yeye vaastavik charr kewal ack prakaar kii ikai kaa pratinidhitva karate hain, jise lekhakon ney praathamik prastaavon koo bulaane key liye chunaa haye.
lagbhag usee samay ludwig witzenstein ney apane 1922 key kaary maarg logico-philosophicus mein isi tarah key vichaar vikasit kieh
witzenstein ney satya-saarani vidhi kaa bhee prastaav rakhaa. apane 4.3 seey 5.101 mein, witzenstein ack aseemit schafer stroke koo apani maulik taarkik ikai key roop mein apanaata haye aur phir dou charr (5.101) key sabhi 16 karyon koo soochibaddh kartaa haye.
matricks-aeye-trooth-table kii dhaarana tarsky key kaam mein 1940-1950 s key roop mein dair seey dikhaai detee haye, e.jee. unake 1946 key soochkaank "matricks, dekhiyeh satya talika"
russell kii shankaaen.
russell ney apane 1920 key "ganitiya darshan kii shuruat" mein "anant aur taarkik prakaron key swayamsiddh" key liye ack puuraa adhyaay samarpit kiya haye jisamen vaha apani chintaon koo vyakt karate hainh "abb prakaron kaa siddhant dridhata seey hamaare vishay key samaapt aur kuchh hisse seey sambandhit naheen haih iss siddhant kaa adhikansh hissa abhee bhee aspasht, bhramit aur aspasht haye. lekin "kuchh" prakaar key siddhant kii aavashyakta siddhant key sateek roop kii tulanaa mein cumm sandigdh haye aur anant key swayamsiddh key sambandh mein iss tarah key kuchh siddhant kii aavashyakta koo dekhana vishesh roop seey aasaan haye.
russell ney reducibility key swayamsiddh siddhant koo chhod diyaah "princia mathematesa" (1927) key dusare sanskaran mein unhone witzenstein key tark koo sweekaar kiya. apane parichay kii shuruat mein vaha ghoshana karate hain kii "isamen koee sandeh naheen hoe sakata haye... kii vaastavik aur spasht charr key beach antar kii koee aavashyakta naheen haye...". abb vaha poori tarah seey matricks dhaarana koo apanaata haye aur ghoshana kartaa haye kii "ack kaary kewal apane moolyon key madhyam seey ack matricks mein dikhaai dey sakata haye" (lekin ack futnote mein demersah "yeh hraas key swayamsiddh kaa sthaan letaa haye (kaafee paryaapt roop seey naheen)"). isake alawa, unhone "matricks" kii ack naee (sankshipt, saamaanyikrit) dhaarana kaa parichay diyaa, joe kii "taarkik matricks" haye. . . jisamen koee sthiraank naheen hotaa haye. iss prakaar "pee"."q" ack taarkik matricks haye. iss prakaar russell ney vastutah hraas key swayamsiddh siddhant koo chhod diyaa haye, lekin apane antim paragraph mein vaha kahate hain kii "hamaare vartamaan adim prastaavon" seey vaha "anumanatmak sambandh aur suvyavasthit sambandh" praapt naheen curr sakate hain aur maanate hain kii yadi hraas key swayamsiddh siddhant koo badalane key liye ack nayaa swayamsiddh siddhant haye tou isaki khoj kii jaani baaki haye.
saral prakaron kaa siddhant.
1920 key dashak mein, leone chwisteck aur frank pee. ramsey ney dekhaa kii, yadi koee dushchakra siddhant koo chhodane key liye taiyar haye,
prakaron key vistrit siddhant" mein prakaron key staron kaa padanukram dhwast kiya jaa sakata haye.
parinami pratibandhit tark koo saral prakaron kaa siddhant yaa shayed adhik samanya roop seey, saral prakaar kaa siddhant kahaa jaataa haye. saral prakaar key siddhant key vistrit sutrikaran 1920 key dashak key anta aur 1930 key dashak kii shuruat mein prakaashit kiye gaye they.
aar dwara. carnep, aff. ramse, doubleu.vee.oh. quine, aur aeye. tarsky. 1940 mein alonzo church (ree) ney ise kewal type kiye gaye lambda calculus key roop mein taiyar kiya. aur 1944 mein godel dwara jaanch kii gaee. inn vikas kaa ack sarvekshan collins (2012) mein paaya gayaa haye.
1940-vartamaan.
1944 mein.
curt godel ney apane 1944 key "russell key ganitiya tark" mein ack futnote mein "saral prakaron key siddhant" kii nimnalikhit paribhasha deeh
unhone (1) saral prakaron kaa siddhant aur (2) swayamsiddh samooh siddhant, "aadhunik ganit kii vyutpatti kii anumati detaa haye aur saath hii sabhi gyaat virodhabhason seey bachata haye" (godel 1944:126); isake alawa, saral prakaron kaa siddhant "ack upayukt vyakhya mein pahale" siddhant "[" siddhant ganit "] kii pranali haye. . . . [aim] koee bhee lakshan kewal bahut spasht roop seey dikhaate hain, haalaanki, kii adim avadhaaranaon koo aage spasht karane kii aavashyakta haye "(godel 1944:126).
curry-howard patrachar, 1934-1969.
curry-howard patrachar pramaan-key-prograam aur sootra-key-prakaar kii vyakhya haye. 1934 mein haskell curry key saath shuru honey vaalaa vichaar aur 1969 mein villium alwyn howard key saath antim roop diyaa gayaa. yeh kaee prakaar key siddhanton key "computational ghatak" koo tarkshastra mein vyutpattiyon seey jodata haye.
haward ney dikhaaya kii type kiya gayaa lambda cullon antargyaanvaadi praakritik katauti (yaani, bahishkrit madhya key kaanoon key binaa praakritik katauti) key anuroop haye. prakaron aur tark key beach sambandh maujooda tarkshastra key liye nae prakaar key siddhanton aur maujooda prakaar key siddhanton key liye nae tarkshastra khojane key liye baad key bahut saare shodh kaa netritva kartaa haye.
dee brune kaa swachaalit, 1967-2003.
nikola govert dee brune ney swachaalit pranali key liye ack ganitiya neenv key roop mein swachaalit prakaar key siddhant kaa nirmaan kiya, joe pramaan kii shuddhata koo satyaapit curr sakata thaa. pranali ney samay key saath prakaar siddhant key roop mein vikasit aur visheshtaon koo jodaa.
martin-loaf kaa antargyaanvaadi prakaar siddhant, 1971-1984.
prati martin-loaf ney ack prakaar kaa siddhant paaya joe aashrit prakaron koo pesh karke vidheya tark key anuroop thaa, jise antargyaanvaadi prakaar siddhant yaa martin-loaf prakaar siddhant key roop mein jaanaa jaane lagaa.
martin-loaf kaa siddhant praakritik sankhyaon jaise aseemit detta sanrachanaon kaa pratinidhitva karane key liye prerak prakaron kaa upayog kartaa haye.
martin-loaf dwara apane siddhant kii prastuti mein anuman aur nirnayon key niyamon kaa upayog karna bhavishya key siddhanton koo prastut karane key liye maanak bunn jaataa haye.
kokwand aur huet kaa nirmaan kaa cullon, 1986.
thiyari kokwand aur gerard huet ney nirmaan key cullon kaa nirmaan kiya, joe karyon key liye ack aashrit prakaar kaa siddhant haye. prerak prakaron key saath, ise "prerak nirmaan kaa cullon" kahaa jaayega aur yeh see. oh. kyu. aur dublepan kaa aadhar bunn jaayega.
barendrags lambda cube, 1991.
lambda cube ack nayaa prakaar kaa siddhant naheen thaa, balki maujooda prakaar key siddhanton kaa vargeekaran thaa. ghana key aathh konon mein kuchh maujooda siddhant shamil they jinamen sabse nichale koney mein kewal type kiye gaye lambda calculus aur uchchatam parr nirmaan kaa calculus shamil thaa.
pehchaan pramaan advitiya naheen hain, 1994.
1994 seey pahale, kaee prakaar key siddhantkaron ney socha thaa kii ack hii pehchaan prakaar key sabhi shabd samaan they. yaani, sub kuchh prativartita thee. lekin martin hoffman aur thomas streacher ney dikhaaya kii pehchaan key prakaar key niyamon key anusaar isaki aavashyakta naheen thee. apane pepper mein, "samooh model pehchaan pramaan kii vishishtata kaa khandan kartaa haye", unhone dikhaaya kii samaantaa key shabdon koo ack samooh key roop mein model kiya jaa sakata haye jahaan shoonya tatva "prativartakta" thaa, jodd "pargamansheelta" thaa aur nishedh "samroopata" thee. 
isane shodh kaa ack nayaa kshetra khola, jahan shreni siddhant koo pehchaan key prakaar parr lagu kiya gayaa thaa.

