ganit kaa arastu yathaarthvaadi darshan

ganit key darshan mein, arastu yathaarthvaad kaa maanana haye kii ganit samroopata, nirantarta aur vyavastha jaise gunon kaa adhyayan kartaa haye jinhen bhautik duniya (yaa kissy anya duniya mein hoe sakata haye) mein tatkaal mahsoos kiya jaa sakata haye. yeh iss dhaarana mein platonism key vipareet haye kii ganit kii vastuein, jaise kii sankhyaaen, ack "amoort" duniya mein maujood naheen hain, lekin bhautik roop seey mahsoos kii jaa sakati hain. yeh naamvaad, kalpanikta aur tarkvaad key vipareet haye kii ganit kewal naamon yaa anuman yaa ganana key tarikon key baare mein naheen haye, balki duniya key kuchh vaastavik pahaluon key baare mein haye.
arastu key yathaarthvaadi daarshanik roop seey sabse mahatvapurna key roop mein shuddh ganit key bajaay vyaavhaarik ganit, vishesh roop seey ganitiya pratiroopan parr jore dete hain. maark laing kaa tark haye kii "arastu yathaarthvaad ganitiya tathyon koo vigyaan mein vishisht ganitiya vyakhyaon mein vyakhyata banane kii anumati detaa haye" kyonki ganitiya tathya swayam bhautik duniya key baare mein hain. paul thuggard ney arastu yathaarthvaad koo "ganit key vartamaan darshan key roop mein varnit kiya haye joe munn aur vigyaan key baare mein gyaat baaton key saath sabse upayukt haye."
itihas.
halanki aristotal ney ganit key darshan parr vyaapak roop seey naheen likhaa, iss vishay parr unaki vibhinn tippaniyan vishay key baare mein ack susangat drishtikon koo amurtata key baare mein aur sthaan aur ginati kii vaastavik duniya key liye lagu honey key roop mein pradarshit karati hain.
athaarahavin shatabdi taka, ganit kaa sabse aam darshan arastu kaa drishtikon thaa kii yeh "matra kaa vigyaan" haye, jisamen matra koo nirantar (jyaamiti dwara adhyayan kiya gayaa) aur asatat (ankganit dwara adhyayan kiya gayaa) mein vibhajit kiya gayaa haye.
beesavin shatabdi mein ganit key darshan key liye arastu drishtikon durlabh they, lekin penelope maddy dwara "ganit mein yathaarthvaad" (1990) mein aur 2000 seey kaee lekhakon jaise james franklin, annie newstead, donald gillies aur anya dwara punarjeevit kiye gaye they.
sankhyaaen aur sett.
(mool yaa ginati) sankhyaon key baare mein aristotal key vichaar aristotal key iss avalokan seey shuru hotey hain kii ack dher yaa sangrah kii sankhya chuni gaee ikai yaa maap key saapeksh haih 'sankhya' kaa arth haye ack maapi gaee bahulata aur maapon kii bahulata... maap hamesha una sabhi cheejon key liye kuchh samaan honah chaahiye joe yeh maapati haye, jaise.jee. aggar cheejen ghode hain, tou maap 'ghodaa' haye."glain kessler ney ise iss drishtikon mein vikasit kiya kii ack sankhya ack dher aur ack saarvbhaumik key beach ack sambandh haye joe ise ikaaiyon mein vibhajit kartaa haye; udaaharan key liye, sankhya 4 tote key dher aur saarvbhaumik" tote honey "key beach key sambandh mein mahsoos kii jaati haye joe dher koo itane saare tote mein vibhajit kartaa haye.
ack arastu key drishtikon seey, anupaat mukhya sankhyaon seey nikatata seey judey naheen hain. way oonchaai jaisi maatraon key beach sambandh hain. dou oonchaai kaa anupaat dou dravyamaan yaa dou samay antaral key beach key sambandh key samaan hoe sakata haye.
abhijaat varg key loga samuchchay key saath-saath sankhyaon koo bhautik duniya mein tatkaal maanate hain (platonist sansthaon key bajaay). maddy ney tark diyaa kii jaba ack andey kaa dibba khola jaataa haye, tou teen andon kaa ack samooh (yaani, bhautik duniya mein mahsoos kii gaee ack ganitiya ikai) maanaa jaataa haye. haalaanki sabhi ganitiya pravachanon kii yathaarthvaadi vyakhya karane kii aavashyakta naheen haye; udaaharan key liye arastu vidwan khaali samooh aur shoonya koo kalpana aur sambhavatah uchch anantata key roop mein maan sakate hain.
sanrachanaatmak guna.
abhijaat varg key loga gair-sankhyaatmak sanrachanaatmak gunon jaise samroopata, nirantarta aur crum koo sankhyaon key samaan hii mahatvapurna maanate hain. aise guna bhautik vaastaviktaa mein mahsoos kiye jaate hain, aur ganit key bhaagon key vishay hain. udaaharan key liye samooh siddhant vibhinn prakaar kii samroopata koo vargeekrit kartaa haye, jabaki cullon nirantar bhinnata kaa adhyayan kartaa haye. aisee sanrachanaon key baare mein siddh parinam seedhe bhautik vaastaviktaa parr lagu hoe sakate hain. udaaharan key liye euler ney saabit curr diyaa kii conigsburg key saat pulon parr ack baar aur kewal ack baar chalana asambhav thaa.
gyanmimansa.
choonki ganitiya gunon koo bhautik duniya mein mahsoos kiya jaataa haye, isaliye unhein seedhe mahsoos kiya jaa sakata haye. udaaharan key liye, manushya aasaani seey chehare kii samroopata koo samajhate hain.
abhijaat varg key loga ganitiya soch mein amurtata aur aadarshikaran kii bhee bhoomika nibhaate hain. yeh drishtikon aristotal key apane "bhautiki" mein diye gaye bayaan kii or jaataa haye kii munn parivartan kii duniya (bhautiki ii.2.193b31-35) key alawa shareer key kaalaatit gunon koo dhyaan mein rakhate hue vichaar mein una gunon koo 'alag' kartaa haye jinka vaha ganit mein adhyayan kartaa haye. 
ganit key uchch staron parr, abhijaat varg key loga abhijaat key "pashch vishleshan" key siddhant kaa paalan karate hain, jisake anusaar ganitiya prastaav kaa pramaan aadarsh roop seey paathak koo yeh samajhane mein madad kartaa haye kii prastaav kyon sahee honah chaahiye.
arastu yathaarthvaad parr aapattiyan.
abhijaat varg key yathaarthvaad key liye ack samasya yeh haye kii uchch anantataon kaa kyaa vivaran diyaa jaanaa chaahiye, joe bhautik duniya mein mahsoos yaa sakar naheen kiya jaa sakata haye. jarmelo-frankle sett siddhant mein kshamata aur vaastaviktaa key aristotless siddhant koo kaise lagu kiya jaae. maark balaguer likhate hainh
abhijaat varg key loga jawab dete hain kii vigyaan apramaanit saarvbhaumiktaa seey nipat sakate hain; udaaharan key liye rung kaa vigyaan neele rung kii chhaaya seey nipat sakata haye joe kissy bhee vaastavik vastu parr naheen hoti haye. haalaanki isake liye adhikansh abhijaat varg key logon dwara rakhe gaye tatkaal siddhant koo aswikar karane kii aavashyakta hoti haye, joe maanata haye kii sabhi vaastavik sampattiyan tatkaal hain. ganit key ack abhijaat tatvagyaani donald gillies hain joe indriya aur sandarbh key beach fraze key antar key aadhar parr tatkalikta siddhant seey incar karate hain. unhone iss drishtikon kaa upayog ack abhijaat varg key drishtikon seey bahut badey paar-aseem cardinal seey nipatane kii ack vidhi vikasit karane key liye kiya haye.
abhijaat vargavaad key prati ack aur apatti yeh haye kii ganit bhautik duniya key aadarshikaran seey sambandhit haye, naa kii bhautik duniya key saath. aristotal swayam iss tark seey avagat they kii jyaamiti poorna vritton kaa adhyayan karati haye lekin vaastavik duniya mein hoop poorna vritt naheen hain, isaliye aisaa lagata haye kii ganit kuchh gair-bhautik (platonic) duniya kaa adhyayan curr rhaa hoga. abhijaat varg key loga jawab dete hain kii anuprayukt ganit ney aadarshikaran key bajaay sanniktan kaa adhyayan kiya aur isake parinamswarup aadhunik ganit vaastavik cheejon key jatil aakaron aur anya ganitiya sanrachanaon kaa adhyayan curr sakata haye.

