Izinhlobo zezinkolelo-mbono. ithiyori Mathematical. mbono zesayensi

Indlela iyiphi eyeza nezazi zezinkanyezi ezikhuluma ikwazi ukubona nokuzwa ndoda wanamuhla! Futhi kungaba izinkomba ezahlukene kakhulu. Futhi lokhu akumangalisi, ngoba kukhona izinhlobo ezahlukene mbono. Lena ngenxa yokuthi ukuze udale kulona usebenzisa izindlela ezahlukene, futhi ahloselwe tinhlangotsi letehlukene umphakathi wesintu. Ngakho, kukhona imibono yezombangazwe, zezibalo, kwezomnotho, kwezenhlalo. Kodwa ake zonke sihlolisise.

ulwazi olujwayelekile

Le ndlela yokwenza isayensi izwi "inkolelo-mbono" kungaqondakala ngezindlela ezimbili eziyinhloko: emincane futhi ebanzi. Eyokuqala yalezi libhekisela oluphakeme kakhulu inhlangano yolwazi, okunikeza umbono ephelele ukuxhumana neziqinile futhi amaphethini endaweni ethile engokoqobo. Kulokhu, ngoba a umbono wesayensi owawuthandwa kukhona isici ukuba khona uhlelo lobumbano, ubudlelwane okunengqondo phakathi izakhi, hatchability kwayo okuqukethwe kusukela isethi othize kwelwati zinto (kodwa lokhu kufanele kwenziwe ngokuvumelana nezimiso ezithile ngekulandzelana methodological). Yilokho kanye ihlela theory eyisisekelo. Futhi kuyini okungaphansi kwesandla kuyaqondakala ngomqondo ebanzi izwi?

Theory yesayensi kulokhu iqoqo imibono, imibono nezimvo, okuyinto zihloselwe ahumushe umcimbi othile (noma iqembu ezifuze). Awunayo uthole lutho isimanga? Uma ucabanga ngakho, kulesi simo, cishe wonke umuntu zabo mbono. Justice for kuwufanele ethi ingxenye enkulu basonta sphere kwengqondo kwansuku zonke. Siyabonga kubo indoda sesihlela umqondo wakhe wobulungisa, ubuhle, uthando futhi iyini injongo yokuphila, ubudlelwane ubulili, kwesidumbu khona, nokunye okunjalo.

Kungani imfundiso?

Bakhuthaza uhlobo "amaseli" methodological of ulwazi lwesayensi. Imfundiso yesimanje liqukethe ulwazi kuyatholakala kanye nezinqubo eyenziwe ngawo etholwe futhi wafakazela. Okusho ukuthi, it has eyisisekelo "isakhiwo" impahla - ulwazi. Basuke axhumene izahlulelo. Kakade kuzo, ngokuvumelana nemithetho logic, cabangela enze.

Kungakhathaliseki ukuthi iziphi izinhlobo zezinkolelo-mbono ezibhekwa phansi zabo ngaso sonke isikhathi kumelwe babe munye noma ngisho imibono embalwa (imicabango) anikeza amakhambi ezinkinga ezithile (noma eziyinkimbinkimbi yabo yonke). Okungukuthi, ukuze ngokuthi isayensi agcwele, kwanele ukuba umbono evuthiwe kuphela. Njengoba i-geometry isibonelo.

Ingabe kube lula ukuqonda imfundiso?

Ukuze uqale nge siyowuqonda imiqondo okucatshangwayo, izinkinga nemibono. Abakwazi ngokuvamile angena umusho owodwa. Yokuziphendukela okufanayo cishe akunakwenzeka. Ngakho, ukuchaza abuye esekele yayo ngokuvamile ngisho ukubhala imisebenzi yonke. Kwanele ukusebenzisa njengesibonelo imfundiso yokuziphendukela adonsela phansi jikelele okuyinto Newton zavela. Ukuze ucwaningo yayo ebhala umsebenzi voluminous ngo-1987, obizwa ngokuthi "Mathematical Principles of Philosophy Yemvelo". Ukubhala ke wamthatha iminyaka engaphezu kwengu-20. Kodwa lokhu akusho ukuthi imfundiso eziyisisekelo liyinkimbinkimbi ngendlela yokuthi bangaqondi isakhamuzi abavamile.

Ngokuyinhloko-ke, kufanele kuqashelwe ukuthi kungenzeka le nkolelo-mbono kufanele ngokufingqiwe eziningana kwendikimba (futhi, ngokulandelana, onomfutho) ifomu. Le ndlela inikeza uzothola kuzo zonke ezincane, shu, futhi ngokuvamile lakhishwa kubakaki ulunge kangakanani izimpikiswano bokusekela. Ngaphezu kwalokho, njengoba kushiwo ngaphambili, umuntu ngamunye esingokwemvelo ukwakha imibono yazo, okuyizinto nje okungaqondile ka okwamehlela ukuhlaziywa yayo. Ngakho-ke, uma uthanda ukukuqonda nesayense sibe yinkimbinkimbi futhi imisebenzi njalo lwenziwa.

izinhlobo zezinkolelo-mbono

Zihlukaniswa ngesisekelo isakhiwo zabo, nakho kusekelwe izindlela wokwakha ulwazi theory. Ukunikeza lezi zinhlobo mbono:

• Axiomatic.
• Inductive.
• Esicabanga ukuthi kungaqhamuka-deductive.

Ukuze ngamunye wabo isebenzisa imininingo egciniwe ayo, okuyinto uvezwa uhlobo izindlela ezintathu ezahlukene.

ithiyori axiomatic

imibono enjalo imane nime niqinile isayensi kusukela ezinsukwini zasendulo. Ziyakwazi samuntu okukhulu futhi ikwazi ulwazi lwesayensi. Laba bameleli be-edume kakhulu lolu hlobo theory zezibalo. Njengoba izibalo isibonelo formatizirovannuyu. Ngaphezu ke, ukunakwa eside futhi unikwe logic esisemthethweni futhi ezinye amagatsha physics (wokushintsha kwamandla nokwakheka kwezinto, electrodynamics kanye Mechanics). Isibonelo Classic of Kulokhu iyona geometry Euclidean. Ukuze kaningi iphathwa ulwazi hhayi kuphela, kodwa futhi njengoba isibonelo okukhulu ngokwesayensi. Yini ebaluleke kohlaka lolu hlobo?

Lapha, ezithakazelisa kakhulu yizici ezintathu: postulates (axioms), ukubaluleka ukuboniswa (theorem) kanye nobufakazi (imithetho, tiphetfo). Kusukela ngaleso sikhathi, i-enjini kanye nomklamo izisombululo kakhulu ukushintsha. A ezinezithelo ngokukhethekile kule ndaba kwaba sekhulwini lama-20. Khona-ke athuthukile njengendlela ndlela entsha futhi ezingeni eliyisisekelo yolwazi (imfundiso yokuziphendukela okungenzeka inganikelwa njengesibonelo). Bayaqhubeka nokwakha khona manje, kodwa kuze kube manje akukho lutho kungaba kakhulu vula ekuphileni kwethu.

ithiyori exhasa

Kukholakala ukuthi abekho ifomu okumsulwa, ngoba ayinikeli ulwazi apodictic nenengqondo umsindo. Ngenca yaloko bantfu batsi, kwakusho ukuthini-ke lezi zindlela exhasa. Isici zingabantu ngokuyinhloko ngesayensi yemvelo. Lesi simo siye athuthukile ngenxa yokuthi lokhu lapho ungaqala ngokuhlolwa kanye namaqiniso, futhi siqede ngokuvamile theory.

Nakuba kuyaqapheleka ukuthi eminyaka ambalwa adlule eyeza nezazi zezinkanyezi ezikhuluma exhasa babe zithandwa kakhulu. Kodwa ngenxa usayizi ayisebenzisele okujabulisa yesayensi babeka phezu backburner. Phela, cabanga ngendlela ukuze bahlanganise le nkolelo-mbono ecatshangelwayo, uma safika ngendlela eziwusizo! okukhipha Inductive ngokuvamile ziqala ngokuhlaziya nokumadanisa etholwe ngesikhathi sokuhlola noma ukubheka kwabanye idatha. Uma uthola into efanayo noma ezivamile ke basuke generalized njengoba isikhundla jikelele.

ithiyori yezinto-deductive

Ziyakwazi ethize ukuze ngesayensi yemvelo. UMdali lolu hlobo ubhekwa uGalileo Galilei. Ngaphezu kwalokho, naye wabeka izisekelo nesayensi zokuhlola. Ngemva kwalokho, ziye zasetshenziswa phakathi inombolo enkulu zesayensi, aba nesandla ekuthuthukeni kwalo sokuhlanganiswa udumo zamanje. Ingqikithi wabo ukuthi umcwaningi ubeka phambili kokuqagela ngokugqamile, iqiniso zazo, akwaziwa. Khona-ke umbono usebenzisa i-deductive indlela corollaries zihlobene. Le nqubo iyaqhubeka kuze kube yilapho, lapho kutholakala izitatimende enjalo ukuze ikwazi kuhlobene nezinga okwenzeka. Uma ukuhlolwa enokwehla kuqinisekisa nokwanela yayo, kuphothulwe ngokuthi umbono wokuqala yayingacacile lesifanele.

Yini izingxenye kufanele ibe umbono wesayensi owawuthandwa?

Kunezinhlobo eziningi. Ukuze ugweme ukudideka, sithatha njengesisekelo lowo Shvyrov eziphakanyisiwe. Izingxenye kwalo elandelayo ziyisibopho:

• Kokuqala isisekelo enokwehla. Kufaka elotshiwe kuze kube manje amaqiniso nolwazi, okuyinto zazitholakala ngenxa ucwaningo futhi izifundo zidinga.
• Kokuqala isisekelo theory. Ngalokhu ehloselwe sebuningini eyinhloko axioms postulates nekucabangela kwemithetho jikelele ukuthi sekukonke uvumele ukuchaza ephelele yengxoxo into ukucabangela.
• Logic. Lokhu kubhekisela ukusungulwa nohlaka okufunyenweko ubufakazi.
• Isethi izitatimende. Lezi zihlanganisa ubufakazi ezakha ngobuningi ulwazi olwalukhona.

ukusetshenziswa

Kumele kuqashelwe ukuthi le nkolelo-mbono isisekelo ekutadisheni eziningi izinqubo, kanye nemikhuba ehlukahlukene. Futhi kungenziwa yakhiwa ngesikhathi esifanayo futhi phezu isipiliyoni esiwusizo, futhi ngesisekelo ukucabanga bajule. Ngakho-ke, kukhona, isibonelo, izinhlobo ezahlukene imfundiso yokuziphendukela umthetho. Ngaphezu kwalokho, kufanele kuphawulwe ukuthi omunye futhi ngendaba efanayo lingachazwa nge ezingeni obuhlukahlukene, futhi izici zayo, ngokulandelana, ngeke ifane.

Kwezinye izindawo, kuyisiko amenable ukuba Standardization, njengoba kufakazelwa izinhlobo ithiyori kwezomnotho, futhi ngesikhathi esifanele ucacisa izinkomba entsha. Noma kunjalo, eziningi zoMthetho ngaphakathi kubo namanje edonsela abalandeli ukugxeka. Nakuba ezinye ezicatshangwayo (futhi ekugcineni izisekelo kwezesayensi) ngezinye izikhathi nje kudingeka buthelela ethile yolwazi. Ngaphambi zadalwa womuntu umsuka imfundiso yokuziphendukela Lamarck futhi Darwin, i ngezigaba olubanzi eziphilayo lwenziwe. Lolu cwaningo lezi zici bekulokhu emlandweni wesayensi. Njengoba kuboniswe yile isiyalo, ukuthuthukiswa egcwele inkolelo-mbono (ezazihlanganisa ukuguqulwa yayo, futhi intuthuko, ngcono kanye extrapolation ezindaweni ezintsha) ngokuhamba kwesikhathi kungenziwa welulela kwelinye leminyaka.

Verity

Isici esibalulekile nganoma yisiphi theory isiqinisekiso salo esisebenzayo lapho enquma degree of ubuqiniso bayo. Lapha, ngokwesibonelo, siba theory ocacile zezombusazwe, othi kulesi simo kufanele wenze kanje ngandlela-thile. Uma kungenjalo esisebenzayo ukuqinisekisa noma ukuphika ukusebenza yayo, isinqumo isicelo yayo amanga nabantu, wanika igunya.

Futhi esimweni lapho kukhona abanye ubuqiniso maqondana ke, isivele kungenzeka ukutadisha isipiliyoni ekhona futhi uthathe isinqumo esifanele ekutheni ukuba noma cha nekuwusebentisa. Le sevisi inikeza eside ukuhlaziya theory. Nge indlela athuthukiswe ngaphakathi it can, usebenzisa indlela yezesayensi ukubala ematfuba kusetjentiswa ngemphumelelo, kanye indawo lapho uthola "amagugu afihliweko."