Zango of Zeno of Elea

Zenon Eleysky - logician isiGrike kunye bulumko, nto leyo eyaziwa kakhulu ngenxa eziphikisanayo bakhe, ogama njengentlonipho yokumbulela. ubomi wakhe kakhulu kwaziwa. Wakubo Zeno - Elea. Kwakhona imisebenzi uPlato sobulumko ekhankanywe intlanganiso kunye uSocrates.

Malunga 465 BC. e. Zeno wabhala incwadi, nto leyo ekubaliswa zonke iingcamango zabo. Kodwa ke, ngelishwa, unanamhla zange ayifumane i komsebenzi. Ngokutsho legend, sobulumko wafa edabini kunye uzwilakhe (yezizathu intloko Elea Niarchos). Lonke ulwazi malunga Elea eqokelelweyo kancinci kancinci: kwimisebenzi zikaPlato (wazalwa kwiminyaka engama-60 kamva, Zeno), Aristotle uDiogenes Laertes, owabhala kwiinkulungwane ezintathu kamva, nencwadi iibhayografi le zobulumko zamaGrike. Ezakhankanywa Zeno, naye ngemisebenzi abameli kamva yesikolo bulumko yamaGrike: Themistius (.. kwinkulungwane 4 BC), Alexander Afrodiyskogo (.. yesi-3 BC), kwakunye Philoponus kunye Simplicius (zombini owayephila ngenkulungwane yesi-6 BC.). . Ngaphezu koko, i data kwezi ziyavumelana kakuhle njalo-nye, ukuba unako ukuphinda zonke iingcamango sobulumko. Kweli nqaku, siza kukuxelela malunga zango ka Zeno. Makhe siqale.

zango ubeka

Ukususela ngexesha isithuba kaPythagoras kunye nexesha kuqwalaselwa kuphela ukusuka kwindawo imbono lwemathematika. Oko kukuthi, kwakucingwa ukuba sakhiwa ezininzi amanqaku kunye amanqaku. Noko ke, kufuneka yepropati kulula ukuziva kunokuba ukumisela, ezizezi "phambili". Ezinye zango of Zeno ingqina ukuba ayikwazi kwahlulwa ibe amanqaku okanye amachaphaza. Ukubonisana sobulumko lumi ngolu hlobo: "Masithi ukuba saba qheke kude kube sekupheleni. Ke oyinyaniso kuphela elinye eneenketho ezimbini: noba sifumana i okuseleyo ubukhulu sincinane kunokwenzeka okanye amalungu ukuba ayahlukahlukenanga, kodwa mda ngangenani lazo, okanye ulwahlulo asikhokelele wakuqotywa ixabiso ukususela ekuqhubekekeni, ukuba bomzi, kufuneka ngaku phantsi kwazo naziphi na iimeko . Akangekhe komnye liyohluleka, kunye nezinye - akukho. Ngelishwa, bobabini umphumo kakhulu etyeni. Imvelaphi yokuba inkqubo ngokucandeka ukuze uphele de amasalela iye iinxalenye kokuba ixabiso. Kwaye okwesibini, kuba kwimeko enjalo iya kuqala yonke akhiwa nto. " Simplicius zathi le ngxoxo Parmenides, kodwa kubonakale ukuba umbhali wayo - Zenon. Ngena ku.

zango Zeno ngayo motion

Bona ingqalelo kuninzi iincwadi bulumko njengoko ukungena dissonance nobungqina ingqiqo Eleatic. Ngokumalunga intshukumo, kukho indida zilandelayo Zeno: "Arrow", "dichotomy", "Achilles" yaye "Amanqanaba". Baya kuthi ngenxa Aristotle. Makhe sihlolisise ngokweenkcukacha.

"Arrow"

Elinye igama - umyinge Zeno kephofu. Bulumko ithi na into mhlawumbi eyayimi ngxi okanye ihamba. Kodwa akukho ityhalela phambili, ukuba indawo ahlala kuyo i mileage ngokulinganayo. Ngaxa lithile, utolo achukumisayo kwindawo enye. Ngoko ke, kuyo akasuki. Simplicius yaqulunqa leli phuzu ngendlela emfutshane: "Flying into ithatha ilingana indawo isithuba, kwaye kuthatha ulingana indawo isithuba, hayi ezihambayo. Ngoko ke, boom oba. " Himalia Felopon yasebenza embodiments efanayo.

"Dichotomy"

Kuthatha indawo yesibini kuluhlu "kephofu Zeno kaThixo". Oku ifundeka ngolu hlobo lulandelayo: "Ngaphambi isixhobo aqale intshukumo, uya kuba nako ukuya kumgama othile, kufuneka boyise kwisiqingatha ndlela, ngoko ke isiqingatha esiseleyo, njalo njalo infinitum ad ... Ekubeni kwisiqingatha ingxenye ngokwemizi ngokuphindaphindiweyo kumgama lonke ixesha iba anesiphelo, kwaye inani amaqhosha lwedatha ongapheliyo, akunakwenzeka ukuba boyise umgama ngexesha ezisikelwe. Kwaye le ngxoxo lisemthethweni zombini imigama ezincinane izantya eziphezulu. Ngoko ke, nayiphi na intshukumo akunakwenzeka. Oko kukuthi, nembaleki nkqu ukuqala. "

Le indida ke eneenkcukacha kakhulu wathi Simplicius, echaza ukuba kulo mzekelo, ixesha ezisikelwe kuyimfuneko ukwenza inani olungenasiphelo of iqatha. "Lowo uza nantoni na, kungakhokelela amanqaku, kodwa inani ongapheliyo abakwazi Unalungelo okanye ukubala." Okanye, njengoko ziqulunqwe Philoponus, inani olungenasiphelo of athile.

"Achilles"

Eyaziwa ngokuba indida yokuba ufudo Zeno kaThixo. Le ngxoxo ithandwayo bulumko. Le intshukumo indida Achilles kukhuphisana ugqatso ufudo, elinikwa ekuqaleni ungumlwelwe encinane. Indida kukuba amajoni zesiGrike akayi kuba nako ukubamba up kunye nofudo, kuba kuqala ukubaleka kakhulu kuya kwinqanaba sokuqaliswa yayo, kwaye uya kuba phezu ingongoma elandelayo. Oko kukuthi, ufudo iya kuhlala phambi Achilles.

Le indida sifana kakhulu ukuya dichotomy, kodwa kukho iyantlukwano engenamda aye ngokuya phambili. Kwimeko dichotomy kwaba ukuqhubeka kwaba bafundi. Umzekelo, imbaleki akunjalo ukuqala kuba andikwazi ukushiya indawo yayo. Kwaye kukho imeko ne Achilles, nokuba imbaleki uzakufumana phantsi ngendlela ukusuka kwindawo, oko andiyi kuza ubaleka.

"Umhlambi"

Ukuba sithelekisa zonke zango ka Zeno kwi iqondo nobunzima, oku kuya kuphuma ophumeleleyo. Yena Kunzima ukunika kwezinye nokuchaza. Simplicius noAristotle wayichaza le impikiswano zale kwaye ayikwazi nge-100% ngokuqinisekileyo bathembele inokuthenjwa. Ukwakhiwa ngokutsha leli phuzu sesi silandelayo: Makhe A1, A2, A3 kwakunye A4 ayinakutshintshwa lilingane ubungakanani imizimba, yaye B1, B2, B3 kunye B4 - umzimba kubungakanani obufanayo njengoko A. I oshukunyiswa imizimba B ukuya ekunene ukuze B ngalunye oludlulayo ke umzuzwana, nto leyo ke lokuphumla lincinane ixesha zonke. Vumela B1, B2, B3 kunye B4 - umzimba twatse A no-B, aze ahambe kuthelekiswa A ukuya ngasekhohlo, ukuqhekeza ngamnye imizimba ngephanyazo.

Kucacile ukuba bonke abane boyise umzimba B1 B. Makhe nganye kwexesha unit, kwathabatha umzimba efanayo ukuze ndiye mnye B. Kulo mzekelo, zonke intshukumo kufuneka units ezine. Noko ke, oko kwakucingwa ukuba iingongoma ezimbini, le yokugqibela yale intshukumo kuba ncinane kwaye ngoko - are ebumbene. Kulo kulandela ukuba umanyano ezine ayahlukahlukenanga lasi ezimbini ebumbene.

"Indawo"

Ngoko uyazi zango ezisisiseko Zeno of Elea. Kuhleli kungqina ngalo yokugqibela, indawo eyaziwa ngokuba "Indawo". Le indida of Zeno Aristotle zobumnini. iingxoxo ezifanayo ziye ezicatshulwe kweli kwimibhalo Simplicius kunye Philoponus kwi BC ngenkulungwane yesi-6. e. Apha iintetho Aristotle malunga nalo mba kwixesha Physics bakhe: "Ukuba kukho indawo, ukuze ubone indlela apho ibekwe khona? Ubunzima, owabakhoyo Zenon, ufuna ingcaciso. Ekubeni yonke into ikhona na indawo, kuyacaca ukuba kwindawo ukuba indawo, njalo njalo. D. To Infinity. " Ngokutsho kweentanda ezininzi, kukho imangalisayo apha kuba akukho namnye langoku ayahlukanga ngokwakhe kwaye equlethwe ngokwayo. Philoponus ukholelwa ukuba ngokugxila self-ziphikisana ingqiqo ka "indawo", Zeno wayefuna ukuyiphikisa ngobhalo ubuninzi.