Pov thawj yog tsis yuav tsum tau: cov piv txwv ntawm lub axiom

Yuav ua li cas yog qab lub mysterious lo lus "axiom", los ntawm qhov uas nws tuaj thiab nws txhais li cas? Schoolboy 7-8 qib yooj yim teb lo lus nug no vim hais tias tsis ntev los no, nrog rau txoj kev loj hlob ntawm lub hoob pib ntawm lub dav hlau geometry, nws twb raug tej kev ua hauj lwm: "Uas nqe lus no yog hu ua axioms, muab piv txwv." Ib tug zoo xws li cov nqe lus nug ib tug neeg laus yog yuav ua rau poob ntsej muag. Qhov ntau lub sij hawm kis tau txij li thaum txoj kev tshawb no, qhov nyuaj nws yog los nco ntsoov rau hauv lub tsim ntawm science. Txawm li cas los, lo lus "axiom" yog feem ntau siv nyob rau hauv niaj hnub siv.

lub ntsiab txhais

Yog li ntawd yog dab tsi yog hu ua axioms ntawm kev pom zoo? Piv txwv ntawm axioms yog heev ntau haiv neeg thiab tsis tag rau cov ib cheeb tsam ntawm science. Hais tias lub sij hawm los ntawm lub Greek lus thiab lus txhais tau tias "coj txoj hauj lwm".

Ib tug nruj ntsiab txhais ntawm lub sij hawm hais tias axiom - lub ntsiab tswv yim sib cav txog tej yam kev tshawb xav hais tias tsis yuav tsum tau ntawv pov thawj. Muaj yog ib tug ntau notion nyob rau hauv kev kawm txog zauv (tshwj xeeb tshaj yog geometry), logic, philosophy.

Ntau ancient Greek Aristotle hais tias qhov cuab kev tseeb, cov pov thawj yog tsis yuav tsum tau. Piv txwv li, tsis muaj ib tug xav tias lub hnub ci yog tsuas pom thaum lub sij hawm ib hnub. Kuv tsim no ziag no los ntawm lwm daim ntawv thom nug - Euclid. Ib qho piv txwv ntawm lub axiom txog thaum uas tig mus kab ntawd yeej tsis hla nws.

Thaum lub sij hawm, lub ntsiab txhais hloov. Tam sim no axiom ntaus nqi tsis tau tsuas yog raws li thaum pib ntawm science, thiab lub resulting intermediate raws li ib tug tej yam tshwm sim, uas ua hauj lwm pab raws li ib tug starting taw tes rau ntxiv kev tshawb xav.

Pom zoo los ntawm lub tsev kawm ntawv cov hoob kawm

Cov menyuam kawm ntawv yuav los kawm txog postulates tsis yuav tsum tau kev pom zoo ntawd nyob rau hauv zaj lus qhia kev kawm lej. Yog li ntawd, thaum high school kawm tiav muab ib txoj hauj lwm: "Muab piv txwv ntawm axioms", lawv feem ntau xav tias kev kawm ntawm geometry thiab algebra. Ntawm no yog cov piv txwv ntawm ib qho lus teb:

• ncaj point muaj, hais tias nws yog kho (ie dag rau ib tug ncaj kab) thiab tsis thov (tsis txhob dag rau ib tug ncaj kab);
• koj muaj peev xwm kos ib tug kab ncaj nraim los ntawm tej yam ob lub ntsiab lus;
• mus ua txhaum lub dav hlau mus rau hauv ob ib nrab-lub dav hlau, nws yog tsim nyog los tuav ib tug ncaj kab.

Algebra thiab xam nyob rau hauv ib tug qhia tau meej heev daim ntawv ntawm xws assertions yog tsis muab, tab sis ib qho piv txwv ntawm lub axiom yuav pom nyob rau hauv cov sciences:

• yam tsawg sib npaug zos rau nws tus kheej;
• chav tsev precedes tag nrho tej yam ntuj tso tus xov tooj;
• Yog hais tias k = l, ces l = k.

Yog li, los ntawm tej yam yooj yim theses yog tswvcuab ntau tshaj cov ntsiab lus, ua qhov kev tshawb nrhiav thiab tshem tawm cov theorem.

Lub tsev ib scientific theory raws li axioms

Yuav kom tsim ib tug scientific theory (tsis muaj teeb meem dab tsi zoo ntawm kev tshawb fawb nyob rau hauv nqe lus nug), uas yuav tsum tau hauv paus - lub tsev blocks los ntawm uas nws yuav muaj. Lub essence ntawm lub axiomatic hom: tsim ib tug glossary ntawm cov nqe lus, ib qho piv txwv ntawm lub axiom formulated rau lub hauv paus ntawm uas qhia txog cov seem postulates.

Kev glossary yuav tsum muaj tswv yim, piv txwv li cov uas yuav tsis tau txhais ntawm lwm yam:

• Sequentially piav txhua lub sij hawm, cuag nws cov nuj nqis, mus txog tej kev kawm bases.
• Cov kauj ruam tom ntej - cov cim ntawm ib tug tub ntxhais txheej neeg pab leg ntaubntawv, uas yuav tsum muaj txaus rau lub pov thawj ntawm qhov seem uas assertions ntawm kev tshawb xav. Sami tib yooj yim postulates txais tsis ua neeg ncajncees.
• Cov kauj ruam kawg - thiab kev tsim thiab cov zajlus kom xaus ntawm qhov kev tshawb xav.

Postulates ntawm lub ntau yam sciences

Qhia tsis muaj pov thawj tsis yog tsuas yog nyob rau hauv lub caij nyoog sciences, tab sis kuj nyob rau hauv cov neeg uas yog feem ntau yog ntaus nqi mus rau humanities. Ib tug piv txwv - ib tug philosophy uas qhia ib qho axiom li ib daim ntawv qhia tias koj yuav kawm tau yam tsis muaj tswv yim kev txawj ntse.

Ib qho piv txwv ntawm lub axiom yog tseem nyob rau hauv jurisprudence: "koj yuav tsis txiav txim rau koj tus kheej tus cwjpwm." Raws li nyob rau hauv no kev pom zoo, tso zis pej xeem txoj cai - kev hais plaub ntug impartiality, uas yog, ib tug kws txiav txim plaub tsis tau hnov ib tug cov ntaub ntawv yog hais tias nws yog ncaj qha los yog kov xav nyob rau hauv nws.

Tsis yog txhua txhua noj rau kev tso

Yuav kom to taub qhov txawv ntawm tseeb axioms thiab yooj yim kab zauv, uas tshaj hais tias qhov tseeb, nws yog tsim nyog los soj ntsuam qhov cwj pwm ntawm lawv. Piv txwv li, thaum nws los txog rau kev ntseeg, qhov twg txhua yam yog muab rau tso cai, muaj coob leej ntau tus hauv paus ntsiab lus ntawm tag nrho txoj kev ntseeg uas ib yam dab tsi yog qhov tseeb vim hais tias nws yog tsis yooj yim sua los ua pov thawj. Thiab nyob rau hauv lub scientific zej zog hais tias nws yog tsis yooj yim sua mus xyuas kom txog thaum ib tug tej yam txoj hauj lwm, ntsig txog, nws yuav ua tau ib tug axiom. Kam ntseeg, mus saib rov qab - tias yog dab tsi distinguishes ib tug yeej muaj tseeb tus paub txog.