Lub paradoxes ntawm Zeno ntawm Elea

Zenon Eleysky - Greek logician thiab philosopher, uas yog tsuas yog lub npe hu rau nws paradoxes, npe hu ua nyob rau hauv nws yawm. Nws lub neej yog tsis heev npaum li cas paub. Hometown Zeno - Elea. Tsis tas li ntawd nyob rau hauv tej hauj lwm ntawm Plato lub philosopher hais rooj sib tham nrog Socrates.

Nyob ib ncig ntawm 465 BC. e. Zeno sau tau ib phau ntawv, uas hais tag nrho lawv cov tswv yim. Tab sis, hmoov tsis, mus hnub no nws ho tsis nrhiav ib tug striker. Raws li Legend, lub philosopher tuag nyob rau hauv sib ntaus sib tua nrog rau cov tyrant (txawm lub taub hau Elea Niarchos). Tag nrho cov ntaub ntawv hais txog Elea sau me ntsis los ntawm me ntsis: los ntawm Plato tej hauj lwm (yug 60 xyoo tom qab ntawd, Zeno), Aristotle thiab Diogenes Laertes, uas tau sau peb centuries tom qab, ib phau ntawv ntawm cov ntawv sau txog ntawm lub Greek philosophers. Hais txog Zeno, yog tseem nyob rau hauv tej hauj lwm ntawm lub tom qab cov neeg sawv cev ntawm lub tsev kawm ntawv ntawm Greek philosophy: Themistius (.. 4 xyoo pua BC), Alexander Afrodiyskogo (.. 3 xyoo pua BC), raws li zoo raws li Philoponus thiab Simplicius (ob nyob rau hauv lub 6 xyoo pua BC.). . Ntxiv mus, cov ntaub ntawv nyob rau hauv cov chaw no pom zoo zoo li ntawd nrog txhua lwm yam, hais tias nws yog tau los sis tag nrho cov tswv yim ntawm cov philosopher. Nyob rau hauv no tsab xov xwm, peb yuav qhia rau koj txog lub paradoxes ntawm Zeno. Wb tau pib.

paradoxes poob lawm

Puas tau txij lub era ntawm Pythagoras qhov chaw thiab lub sij hawm xam tau tias yog heev dua lwm yam los ntawm tus taw tes ntawm view ntawm kev kawm txog zauv. Hais tias yog, nws txawm xav hais tias lawv tseem muaj li ntawm ib tug plurality ntawm cov ntsiab lus thiab cov ntsiab lus. Txawm li cas los, lawv muaj ib tug uas yog yooj yim los mus xav tias tshaj los mus txiav txim, uas yog lub "laaj". Ib txhia paradoxes ntawm Zeno proves hais tias nws yuav tsis raug faib mus rau hauv cov ntsiab lus los yog tsuas me me. lub philosopher tus yam yog raws li nram no: "Cia hais tias peb muaj ib tug faib txog rau thaum xaus. Ces yeej muaj tseeb tsuas yog ib tug ntawm ob xaiv: yog peb tau txais ib tug seem ntawm qhov tsawg tshaj plaws tau me me los yog qhov chaw uas yog indivisible, tab sis yog infinite nyob rau hauv lawv cov xov tooj, los yog cov kev faib coj peb mus rau daim tsis muaj nqi vim lub laaj, ua homogeneous, yuav tsum muaj divisible nyob rau hauv txhua yam . Nws yuav ua tsis tau nyob rau hauv ib tug ntawm cov divisible, thiab lwm yam - tsis muaj. Tu siab, ob lub no heev tsis zoo. Keeb kwm ntawm lub fact tias cov fission cov txheej txheem yuav tsis xaus kom txog thaum lub qhov seem muaj feem muaj nqi. Thiab yam thib ob, vim hais tias nyob rau hauv xws li ib tug teeb meem no chiv tag nrho yuav tsum tsim nyob rau tawm ntawm tsis muaj dab tsi. " Simplicius ntaus nqi no sib cav Parmenides, tab sis nws yog ntau dua uas nws sau - Zenon. Los.

Zeno lub paradoxes ntawm cov lus tsa suab

Lawv pom tau hais tias nyob rau hauv feem ntau ntawm cov phau ntawv nyob rau philosophy li nkag mus rau hauv dissonance nrog pov thawj Eleatic kev txiav txim zoo. Nrog hais txog lub zog, muaj cov nram qab no paradox Zeno: "xub", "dichotomy", "Achilles" thiab "qib". Thiab lawv tuaj rau peb ua tsaug rau Aristotle. Cia xyuas lawv nyob rau hauv kom meej.

"Xub"

Lwm lub npe - quantum Zeno paradox. Philosopher hais tias muaj tshaj plaws yog sawv tseem los yog tsiv. Tab sis tsis muaj dab tsi yog nyob rau hauv tsab ntawv tsa suab, yog tias qhov chaw nyob los ntawm ib tug sib npaug zos nqi. Nyob rau tej taw tes, lub tsiv xub yog nyob rau hauv tib lub qhov chaw. Yog li ntawd, nws tsis txav. Simplicius formulated no paradox nyob rau hauv ib tug meej daim ntawv: "Ya khoom occupies sib npaug zos rau ib qho chaw nyob rau hauv qhov chaw, thiab hais tias yuav siv sij hawm sib npaug zos rau ib qho chaw nyob rau hauv qhov chaw, tsis tsiv. Yog li ntawd, cov boom rests. " Himalia Felopon formulated thiab zoo sib xws embodiments.

"Dichotomy"

Nws yuav siv sij hawm ob qhov chaw nyob rau hauv daim ntawv teev "Zeno lub paradox". Nws nyeem raws li nram no: "Ua ntej tus kwv uas pib lub zog, yuav tsum tau mus ib yam nrug, nws yuav tsum kov yeej lub ib nrab ntawm txoj kev, ces cov seem ib nrab, thiab ces rau ad infinitum ... Txij li thaum ib nrab ya los ntawm rov sib cais deb tag nrho cov sij hawm yuav finite, thiab tus naj npawb ntawm daim ntawm cov ntaub ntawv yog infinite, nws yog tsis yooj yim sua los mus kov yeej qhov kev ncua deb nyob rau hauv ib tug finite lub sij hawm. Thiab sib cav no yog siv tau ob qho tib si rau cov me ncua kev thiab siab speeds. Yog li ntawd, tej zog tsis yooj yim sua. Hais tias yog, ib tug neeg khiav tsis tau txawm pib. "

Qhov no paradox yog heev ncauj lus kom ntxaws commented Simplicius, taw kom paub tias nyob rau hauv cov ntaub ntawv no, ib tug finite lub sij hawm yog tsim nyog los ua ib tug infinite tus naj npawb ntawm touches. "Leej twg los rau dab tsi, yuav ua tau, tab sis ib tug infinite tooj yuav tsis ntsuas los yog suav." Los yog, raws li formulated Philoponus, ib tug infinite tus naj npawb ntawm indefinable.

"Achilles"

Tsis tas li ntawd lub npe hu ua lub paradox ntawm Zeno tus vaub kib. Qhov no yog cov feem ntau nrov sib cav ntawm lub philosopher. Qhov no paradox zog Achilles lwv nyob rau hauv cov haiv neeg nrog rau cov vaub kib, uas yog muab rau thaum pib ntawm ib tug me me tsis taus. Lub paradox yog hais tias lub Greek cov tub rog yuav tsis muaj peev xwm mus ntes tau mus nrog cov vaub kib, vim hais tias nws thawj khiav kom deb li deb mus rau lub point ntawm lub community launch, thiab nws mam li yuav nyob rau hauv cov tom ntej no taw tes. Hais tias yog, tus vaub kib yuav yeej ib txwm yuav ua ntej ntawm Achilles.

Qhov no paradox yog heev uas zoo sib xws rau cov dichotomy, tab sis muaj ib tug infinite division mus raws li kev vam meej. Nyob rau hauv cov ntaub ntawv ntawm dichotomy yog regression. Piv txwv li, tib neeg khiav tsis tau pib vim hais tias nws tsis tau tawm nws qhov chaw nyob. Thiab nyob rau hauv ib qhov teeb meem nrog Achilles, txawm yog hais tias tus neeg khiav yuav tau txais nyob rau hauv txoj kev los ntawm ib qho chaw, nws tseem yuav tau khiav tuaj.

"Flock"

Yog hais tias peb piv rau tag nrho cov paradoxes ntawm Zeno rau cov neeg kawm ntawv ntawm teeb meem, qhov no yuav tuaj tawm tus khiav. Nws yog ib qhov nyuaj rau muab nyob rau hauv lwm yam exposition. Simplicius thiab Aristotle piav no sib cav yog fragmentary thiab yuav tsis nrog 100% tseeb cia siab rau nws muaj kev cia siab. Reconstruction ntawm no paradox yog lub nram qab no: Cia A1, A2, A3 thiab A4 yog tsau lub cev sib npaug zos loj, me, thiab B1, B2, B3 thiab B4 - ib lub cev ntawm cov loj tib yam li A. Lub cev B tsiv mus rau hauv txoj cai kom txhua tus B kis tau thiab rau ib tug lub sij hawm ntawd, uas yog qhov tsawg tshaj plaws luv ntawm lub sij hawm ntawm tag nrho cov. Cia B1, B2, B3 thiab B4 - lub cev zoo tib yam rau A thiab B, thiab tsiv mus nyob txheeb ze rau tus A mus rau sab laug, rhuav txhua yam ntawm lub cev nyob rau hauv ib qho instant.

Nws yog pom tseeb tias tag nrho plaub kov yeej B1 lub cev B. Cia peb ib chav tsev lub sij hawm, nws coj tib lub cev rau tso cai nyob rau ib lub cev B. Nyob rau hauv cov ntaub ntawv no, tag nrho cov zog yuav tsum tau plaub units. Txawm li cas los, nws txawm xav hais tias ob lub ntsiab lus, lub xeem rau qhov no yuav tsum tau tsawg heev thiab yog li ntawd - yog indivisible. Los ntawm no nws hais ntxiv hais tias cov plaub indivisible kev sib sau ob indivisible units.

"Qhov chaw nyob"

Yog li ntawd tam sim no koj paub qhov yooj yim paradoxes ntawm Zeno ntawm Elea. Nws tseem mus qhia txog lub caij nyoog kawg no, uas yog lub npe hu ua "Lub qhov chaw". Qhov no paradox ntawm Zeno Aristotle tej cwj pwm. Zoo li cov nqe lus tau raug nplua nyob rau hauv lub ntawmv ntawm Simplicius thiab Philoponus nyob rau hauv lub 6 xyoo pua BC. e. Ntawm no Aristotle hais txog qhov teeb meem no nyob rau hauv nws Physics: "Yog hais tias muaj yog ib qho chaw, yuav ua li cas los mus txiav txim qhov twg nws yog nyob? Cov teeb meem, cov uas tau Zenon, yuav tsum tau piav qhia. Txij li thaum txhua yam uas tau tshwm sim muaj ib qho chaw, nws yog cuab kev tias nyob rau ib qhov chaw yuav yog ib qho chaw, thiab thiaj li nyob. D. Yuav kom infinity. " Raws li feem ntau philosophers, muaj yog ib tug paradox no vim hais tias tsis muaj ntawm cov tam sim no muaj peev xwm tsis yuav txawv los ntawm nws tus kheej thiab muaj nyob rau hauv nws tus kheej. Philoponus ntseeg hais tias los ntawm nws tus kheej-contradictory tswvyim ntawm "qhov chaw", Zeno xav refute lub hom phiaj ntawm multiplicity.