antardnyanvad

ganitachya tattvadnyanat, antardnyanvad kinwa navkalpanavad (purvadnyanvadachya virodhat) haah eka drushtikon aahe, jyamadhye ganeet heey vastunishtha vastavat astitvat asalyacha dawa kelelya moolbhut tattvanchya shodhapeksha purnapane manavanchya rachnatmak mansik kriyakalapancha parinam manale jaate. mhanjech, tarkshastra aanee ganeet heey vishleshanatmak kriyakalap manale jaat naheet jyamadhye vastunishtha vastavikateche sakhol gunadharm ughad kele jaatat aanee lagoo kele jaatat, parantu tyaeivaji vastunishtha vastavikatemadhye tyanche sambhavya swatantra astitva asale taree, adhik jatil mansik rachana sakaranyasathi vaparlya jaanarya antargat susangat paddhatincha vapar manale jaatat.
satya aanee purava.
ganiteey vidhan kharey asanyacha arth kaay aahe yacha arth lavane heey antardnyanvadache moolbhut vaishishtya aahe. brauvarchya mool antardnyanvadamadhye, ganiteey vidhanache satya haah eka vyaktinishth dawa aaheh ganiteey vidhan mansik sanrachaneshi sambandhit asate aanee eka ganitshastradnya keval antardnyanadvare tyaa sanrachanechi vaidhata satyapit karoon vidhanache satya siddha karoo shakato. satyachya antardnyani kalpanechi aspashtta anekada tyachya arthabaddal chukichya arth lavnyas karanibhoot tharate. kleenne vastavadi sthitivarun antardnyani satyachi aupcharik vyakhya kelee, tarihi tyane vastavadi/tattvavadi sthitee nakarlyamule, brauvar heey aupcharikaran arthaheen mhanoon nakarel. tyamule antardnyani satya kahise aspasht rahate. tathapi, satyachi antardnyani kalpana shastriy ganitapeksha adhik pratibandhatmak asalyane, antardnyanine shastriy tarkshastrachya kahee gruhitke nakarli pahijet jenekarun teey jeey kahee siddha karatat teey serve pratyakshat antardnyanidrushtya kharey aahe yachee khatri kelee jaau shakate. heey antardnyani tarkshastrala janm dete.
antardnyanisathi, vishisht gunadharm asaleli vastoo astitvat aahe assa dawa haah assa dawa aahe qee tyaa gunadharmansah ekhadi vastoo bandhali jaau shakate. konatihi ganiteey vastoo hii manachya nirmitichi utpadane manali jaatat aanee mhanunach, ekhadya vastuche astitva tyachya nirmitichya shakyatechya samatulya asate. heey shastriy drushtikonashi virodhabhas aahe, jyamadhye asey mhatale aahe qee ekhadya ghatakache astitva tyachya astitvache khandan karoon siddha kele jaau shakate. antardnyanisathi, heey vaidh nahee; astitvachya khandan yacha arth assa nahee qee tyachya astitvacha dawa karnyasathi aavashyak asalelya anumanit vastusathi rachana shodhane shakya aahe. asha prakare, antardnyanvad haah ganiteey rachanatmakatecha eka prakar aahe; parantu too ekmev prakar nahee.
shastriy tarkshastrapeksha antardnyani tarkshastrat nakaracha arth vegala aahe. shastriy tarkshastrat, vidhanache nakar heey vidhan "chukiche" aahe assa dawa karato; antardnyani vyaktisathi, yacha arth vidhan "khandanyogya" aahe.
asha prakare antardnyanvadamadhye sakaratmak aanee nakaratmak vidhanamadhye vishamata aahe. jarr 'pii' heey vidhan siddha karnyayogya asel, tarr 'pii' nishchitpane nakarta yenar nahee. pann jaree heey dakhavale jaau shakate qee "pii" nakarle jaau shakat nahee, taree haah "pii" chaa purava nahee. tyamule 'pii' heey 'nott-nott-pii' peksha adhik majboot vidhan aahe.
tyachpramane, antardnyani vyaktis 'aaa' kinwa 'buub' asey vatate assa dawa karane mhanje 'aaa' kinwa 'buub' heey 'siddha' kele jaau shakate assa dawa karane hoy. visheshtah, vagalalele madhyam, 'aaa' kinwa 'aaa' nahee, haah kayada vaidh tattva mhanoon swikarla jaat nahee. udaharanarth, jarr 'aaa' heey kahee ganiteey vidhan asel jeey ekhadya antardnyanine adyap siddha kinwa nakarlele nasel, tarr too antardnyani 'aaa' chey satya siddha karnar nahee kinwa 'aaa' chey nahee. tathapi, antardnyani heey manya karel qee 'aaa' navhe tarr 'aaa' kharey asoo shakat nahee. asha prakare antardnyani tarkshastrache sanyojak 'aanee' aanee 'kinwa' heey shastriy tarkshastrapramane dii morganchya niyamanche samadhan karat naheet.
antardnyani tarkshastra amoort satyachya rachanatmakatechi jaaga ghete aanee aadhunik ganitatil aadarsh siddhantachya puravyapasun amoort satyakade sankraman karnyashi sambandhit aahe. tarkik ganan heey satyapeksha, vyutpann prastav prastav parivartananmadhye samarthan rakhoon thevate. tattvadnyanachya anek shalanna, visheshtah michael dametchya vastavadavirodhi tattvadnyanala, tatvik aadhar mhanoon heey ghetale gele aahe. asha prakare, tyache naav vyakt karoo shakel asha pahilya chhapachya ulat, aanee vishisht drushtikon aanee shakhanmadhye lakshat aale aahe (udaa.jee. aspasht sanch aanee pranali), antardnyani ganeet heey paramparikpane sthapit ganitapeksha adhik kathor aahe, jithe, vidamban mhanje, antardnyanvad jyaa moolbhut ghatakanchi nirmiti/khandan/punarbandhani karnyacha prayatna karato teey antardnyanipane dile jaatat.
anant.
antardnyanvadachya vegvegalya sutranmadhye, anantatecha arth aanee vastav yavar anek bhinn sthitee aahet.
sambhavya anant hii sandnya ganiteey prakriyecha sandarbh dete jyamadhye servechee eka antaheen malika asate. pratyek payari purn jhalyanantar, nehmi aanakhi eka payari paar padaychi asate. udaharanarth, mojanichya prakriyecha vichar karah 
vastavik anant haah shabd purn ganiteey vastoocha sandarbh deto jyamadhye anant sankhyene ghatak asatat. eka udaharan mhanje naisargik sankhyancha sanch, 
canterchya sanch siddhantachya rachnet, anek bhinn anant sanch aahet, jyapaiki kahee itaranpeksha mothe aahet. udaharanarth, serve vastavik sankhyancha sanch tyapeksha motha aahe, kaaran naisargik sankhya vastavik sankhyanshi eka-eka-eka sanvad sadhanyasathi tumhi vaparnyacha prayatna karata tee konatihi prakriya nehmich ayashasvi hoilah nehmi anant sankhya asel. naisargik sankhyanshi eka-eka sanvad sadhun thewala jaau shakato assa konatahi anant sanch 'gananiy' kinwa 'gananiy' manla jaato. yapeksha mothe anant sanch 'aganit' asalyache mhatale jaate.
canterchya sanch siddhantamule zarmelo-frankel sanch siddhantachi (zed. eff. see.) svayamsiddha pranali nirman jhaali, jee aata aadhunik ganitacha sarvat samanya paya aahe. antardnyanvad kahee pramanat, canterchya sanch siddhantachi pratikriya mhanoon tayar karnyat aala hota.
aadhunik rachnatmak sanch siddhantamadhye zed. eff. see. pasoon anantatecha svayamsiddha (kinwa yaa svayamsiddhatechi sudharit aavrutti) aanee naisargik sankhyancha sanch samavisht aahe. bahutek aadhunik rachnatmak ganitshastradnya mojmap karnyayogya anant sanchanche vastav swikartat (tathapi, prati-udaharanasathi alekzandar esenin-volpin pahaa).
brauvarne vastavik anantatechi sankalpana nakarli, parantu sambhavya anantatechi kalpana manya kelee.
itihas.
antardnyanvadacha itihas ekonisavya shatkatil ganitatil done vivadanmadhye shodhala jaau shakato.
yapaiki pahila, george canterne kelelya transfinite ankganitacha shodh aanee tyanantar tyache anek pramukh ganitshastradnyanni, jyat sarvat prasiddha tyache shikshak, nishchit kelele finiticist, leopold kronkar yancha samavesh hota, too nakarla.
yapaiki dusare mhanje gottlob freeze yanni sanch siddhantadvare serve ganeet tarkik rachnet aananyacha prayatna keela aanee raselchya virodhabhascha shodh shodh tarun bertrand raselane teey rulavarun utaravale. freezene teen khandanchya nishchit kamache niyojan kele hote, parantu jevha dusra khand chhapanar hota, tevha raselane freezla tyachya virodhabhasavar rekhatanare eka patra pathavale, jyane heey dakhavun dile qee freejchya swa-sandarbh niyamanpaiki eka swayam-virodhabhasi hota. hota khandachya parishishtat, freezene kabool kele qee tyachya pranalichya svayamsiddhanpaiki ekane pratyakshat raselchya virodhabhasala janm deela.
katha sangate, qee too nairashyat budala aanee tyane tharavalyapramane tyachya kamacha tisra khand prakashit keela nahee. davis (2000) adhyay 3 aanee 4: 'fradgeh fracture too breakthroo too discipress' aanee 'canterh' anantatoon valane 'adhik pahanyasathi pahaa."mool kamansathi vanne hazenoort aanee vanne hazenoortche bhashya pahaa.
heey vivad drudhpane jodalele aahet kaaran canterne tyache parinam parmitiy ankganitachya madhyamatoon siddha karnyasathi vaparlelya tarkik paddhati moolatah raselane tyacha virodhabhas tayar karnyasathi vaparlya gelelya paddhatipramanech aahet. tyamule raselcha virodhabhas sodavane kase nivadave yacha thet parinam canterchya transfinite ankganitachya sthitivar hoto.
visavya shatkachya suruvatila I. eae. jeey. brover yanni "antardnyani" padache aanee david hilbert yanni aupcharik padache pratinidhitva kele-vanne hazenoort pahaa. curt godelane 'platonist' mhanoon sandarbhit matey mandali (vividh srot rii godel pahaa). alaan turing vichar karatoh
"tarkshastrachya gair-rachnatmak pranali jyachya aadhare puravyatil serve serve yantrik nasatat, kahee antardnyani asatat". (turing 1939, davis 2004 madhye punarmudran, pru. 210) nantar, stephen kole clean yanni tyanchya 'introduction too metamathematics' (1952) madhye antardnyanvadacha adhik tarkshuddha vichar mandala.
nicolas jissin heey quantum anishchitata, mahitee siddhant aanee velechya bhautikshastracha punarvyakhyan karnyasathi antardnyani ganitacha avalamb karat aahet.

