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Зенон Элейский, его парадоксы и понятия бесконечности

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C A I I I Y E A E N E E E , A A I I A ? A Ae I E N U

E I I I ss O E A A A N E I I * I I N O E

Ieoaai?eeneay oeiea. Ieoaai? iniiaae a?aonoai ?aeeaeeciiai, oeeinioneiai
e iao/iiai oa?aeoa?a n iieeoe/aneei oeeiiii. O?oaeu, i?eienuaaaiua
iau/ii Ieoaai?o, ioiinyony ia oieueei e eaaaiaea?iiio Ieoaai?o, ii
aiiaua e o?oaeai yoie oeieu iaaeaeo 585 e 400 a. aei i. y .

A naiae einiieiae/aneie eiioeaioeee Ieoaai? ioeacaeny io iiienoe/aneie
eaeae ia?ae/iie noanoaioeee, ii?iaeeaoae anth Anaeaiioth. Aai
eiioeaioeey aeoaeenoe/ia, e a iai?yaeaiee iaaeaeo aeaoiy
i?ioeaiiieiaeiuie i?eioeeiaie – ia?aie/aiiia – iaia?aie/aiiia, ia/aoiia
– /aoiia, aaeeiia – iiiaeanoaaiiia, i?yiia – e?eaia, eaaae?aoiia –
i?iaeieaiaaoia – ii aeaeae i?e/eio anyeiai ?acaeoey. Iaei eioa?anoynue
iaoa?eaeueiuie yeaiaioaie, eioi?ua iiaee au aeaoue i?aaenoaaeaiea i
aaiacena ?acee/iuo ninoaaiuo /anoae Anaeaiiie, Ieoaai?, oaea/aiiue
aeoaieei ?aeeaeiciui oa/aieai, ioaaoeaoei A?aoeeth oiai a?aiaie,
no?aieeny aeaoue aeiaaeueioth ea?oeio einiina a oeaeii. Iniiao anaai ii
aeaeae a /enea, i /ai naeaeaoaeuenoaoao aai aeaaec: “Ana anoue /enei”.

Iaeaieaa aaaeiui n?aaee i?eienuaaaiuo ieoaai?aeoeai ioe?uoee auei
ioe?uoea e??aoeeiiaeueiiai a aeaea ianiecia?eiuo io?aceia i?yiie eeiee.
Aiciiaeii, /oi iii auei naeaeaii a nayce n enneaaeiaaieai
aaiiao?e/aneiai n?aaeiaai a:a = a:n, aaee/eiie, eioi?ay eioa?aniaaea
ieoaai?aeoeaa e neoaeeea neiaieii a?enoie?aoee. *aio ?aaii
aaiiao?e/aneia n?aaeiaa aaeeieoeu e aeaieee, aeaoo nayuaiiuo neiaieia?
Yoi aaei e eco/aieth ioiioaiey noi?ii e aeeaaiiaee eaaae?aoa, e auei
iaia?oaeaii, /oi oaeia ioiioaiea ia au?aaeaaony “/eneii”, oi anoue oai,
/oi iu oaia?ue iacuaaai ?aoeeiiaeueiui /eneii (oeaeui /eneii eee
ae?iaueth), a oieueei oaeea /enea aeiioneaeenue ieoaai?aeneie
a?eoiaoeeie. Ae?oaeie neiaaie, e??aoeeiiaeueiua /enea auee ioe?uou,
eiaaea noaei ynii, /oi iaeioi?ua ioiioaiey iaeuecy au?aceoue n iiiiuueth
oeaeuo /enae. Yoi ioe?uoea iciaiaiiaaei e?ooaiea ieoaai?aeneie oi/ee
c?aiey i i?aaenoaaeiinoe ie?a n iiiiuueth oeaeuo /enae e aucaaei ia?aue
e?ecen a enoi?ee iaoaiaoeee.

Yeaaou. Aeeyiea Yeaeneie oeieu (V a. aei i.y.) ia oi?ie?iaaiea
aano?aeoiie iao/iie iunee ia?iiii. Iniiaaoaeue yoie oeieu, Ia?iaieae,
aue ia?aui, eoi no?iai ?acee/ae /oanoaaiiia e oiiiinoeaaaiia, /oi
i?eaaei e iaecaaaeiie eiio?iioaoeee iaaeaeo iiuoii e o?aaiaaieyi ?acoia.
eiaiii iiyoiio yeaaou ia i?eiyee ieoaai?aeneoth aeieo?eio, noaayuoth a
niioaaonoaea anyeie aaue /enei. anee aeene?aoiua iauaeou iiaeii
i?aaenoaaeoue oeaeuie /eneaie. oi eia/a ianoieo aeaei a neo/aa
iai?a?uaiuo aaee/ei, oaeeo, eae aeeeiu, ieiuaaee, iauaiu e.o.ae.,
eioi?ua a iauai neo/aa iiaeii eioa?i?aoe?iaaoue eae aeene?aoiua iaai?u
aaeeieoe, eeoue anee aeiioneaoue nouanoaiaaiea aaneiia/iiai /enea i/aiue
iaeuo yeaiaioia, ec eioi?uo yoe iauaeou ninoiyo. A ea/anoaa ?aaeoeee ia
yoo iineaaeithth eiioeaioeeth Caiii Yeaeneee (?iae. iaaeaeo 495 e 480
aa. aei i.y.) noi?ioee?iaae /aou?a ia?aaeiena, eeethno?e?othueo
iaaiciiaeiinoue aaneiia/iie aeaeeiinoe e anyeiai aeaeaeaiey, anee
iuneeoue i?ino?ainoai e a?aiy ninoiyueie ec iaaeaeeiuo /anoae. Iauay
oeaeue aai a?aoiaioia iieacaoue oa iaeaiinoe, e eioi?ui i?eoiaeyo,
eiaaea iuoathony iieo/eoue iai?a?uaiua aaee/eiu ec aaneiia/ii iaeuo
/anoeoe, acyouo a aaneiia/iii iiiaeanoaa.

En/eneaiea aaneiia/ii iaeuo aaaeao naia ia/aei io eiooeoeaiiai
i?aaenoaaeaiey a?aeia i iai?a?uaiinoe, iaoaiaoe/aneie aaneiia/iinoe e
i?aaeaea, a oaeaea io oao o?oaeiinoae, n eioi?uie iie noieeioeenue i?e
iiiuoeao yaii ii?aaeaeeoue yoe iiiyoey. Yoe o?e iiiyoey auee ei??aeoii
ii?aaeaeaiu eeoue a XIX a., eiaaea iaoaiaoeee caoioaee
nenoaiaoece?iaaoue aeinoeaeaiey naiae iaoee, e ei i?eoeinue
ia?aniio?aoue iniiaaiey, /oiau iiaeaanoe iiae iaoaiaoe/aneia caeaiea
i?i/iue ooiaeaiaio.

*enea e aaiiao?e/aneea aaee/eiu. Iu aeaeaee, /oi ieoaai?aeoeu
oiiaeiaeyee /enea aaiiao?e/aneei oi/eai: aaeeieoeo – iaeiie oi/ea,
iaeioi?ia ae?oaia /enei – a?oiia oi/ae, ia?acothueo iaeioi?oth
aaiiao?e/aneoth oeao?o. Eaaeaeia /enei o ieo auei aeene?aoiui iaai?ii
aaeeieoe; oaeei ia?acii, ieoaai?aeneay a?eoiaoeea ia?aie/eaaeanue
eco/aieai iieiaeeoaeueiuo oeaeuo /enae e ioiioaiee oeaeuo /enae, eioi?ua
ia n/eoaeenue /eneaie.

; iii ia au?aaeaaony a aeaea ioiioaiee oeaeuo /enae e, cia/eo, aiiaua
ia eiaao noaoona a ieoaai?aeneie a?eoiaoeea. Noi?iia e aeeaaiiaeue ia
eiatho iauae aaeeieoeu ecia?aiey e iacuaathony i a n i e c i a ? e i u
i e. Acaeiiia niioaaonoaea iaaeaeo aaee/eiie e /eneii, ciaeiiia
ieoaai?aeoeai, ieacaeinue ia?ooaiiui. Anee eaaeaeiio /eneo niioaaonoaoao
iaeay aeeeia, oi eaeea /enea ioaeii niiinoaaeoue ianiecia?eiui
aaee/eiai?

Ia?aaeienu Caiiia e iiiyoea aaneiia/iinoe. Eiaiii a nayce n ioe?uoeai
ianiecia?eiuo aaee/ei a a?a/aneoth iaoaiaoeeo i?iieeei iiiyoea
aaneiia/iinoe. A naieo iieneao iauae aaeeieoeu ecia?aiey aeey anao
aaee/ei a?a/aneea aaiiao?u iiaee au ?anniio?aoue aaneiia/ii aeaeeiua
aaee/eiu, ii eaeay aaneiia/iinoe i?eaiaeeea eo a aeoaieia niyoaiea. Anee
aeaaea ?annoaeaeaiey i aaneiia/iii i?ioiaeeee oniaoii, a?aee a naieo
iaoaiaoe/aneeo oai?eyo anaaaea iuoaeenue aai iaieoe e eneeth/eoue. Eo
cao?oaeiaiey ia?aae yaiui au?aaeaieai aano?aeoiuo iiiyoee aaneiia/iiai e
iai?a?uaiiai,i?ioeaiiieiaeiuo iiiyoeyi eiia/iiai e aeene?aoiiai, y?ei
i?iyaeeenue a ia?aaeienao Caiiia Yeaeneiai.

iiae/a?eiooue i?ioeai?a/ey a iiiyoeyo aeaeaeaiey e a?aiaie, ii yoi
aiana ia iiiuoea ?ac?aoeoue oaeea i?ioeai?a/ey.

Aii?ey “Aoeee e /a?aiaoa” i?ioeainoieo eaeaa aaneiia/iie aeaeeiinoe
i?ino?ainoaa e a?aiaie. Auno?iiiaee Aoeee ni?aaioaony a aaaa n /a?aiaoie
e aeaai?iaeii i?aaeinoaaeyao ae oi?o. Iiea ii i?iaaaeeo ?annoiyiea,
ioaeaeythuaa aai io oi/ee ioi?aaeaiey /a?aiaoe, iineaaeiyy i?iiiecao
aeaeueoa; ?annoiyiea iaaeaeo Aoeeeii e /a?aiaoie nie?aoeeinue, ii
/a?aiaoa nio?aiyao i?aeiouanoai. Iiea Aoeee i?iaaaeeo ?annoiyiea,
ioaeaeythuaa aai io /a?aiaoe, /a?aiaoa niiaa i?iiiecao aua iaiiiai
aia?aae, e o. ae. Anee i?ino?ainoai aaneiia/ii aeaeeii , Aoeee ieeiaaea
ia niiaeao aeiaiaoue /a?aiaoo. Yoio ia?aaeien iino?iai ia o?oaeiinoe
noiie?iaaiey aaneiia/iiai /enea ana aieaa iaeuo aaee/ei e iaaiciiaeiinoe
eiooeoeaii i?aaenoaaeoue naaa, /oi yoa noiia ?aaiyaony eiia/iie
aaee/eia.

, aua?aiiiai neieue oaiaeii iaeui.

Ia?aaeien “No?aea” iniiaai ia i?aaeiieiaeaiee, /oi i?ino?ainoai e a?aiy
ninoaaeaiu ec iaaeaeeiuo yeaiaioia, neaaeai “oi/ae” e “iiiaioia”. A
iaeee “iiiaio” naiaai iieaoa no?aea iaoiaeeony a iaeioi?ie “oi/ea”
i?ino?ainoaa a iaiiaeaeaeiii ninoiyiee. Iineieueeo yoi aa?ii a eaaeaeue
iiiaio aa iieaoa, no?aea aiiaua ia iiaeao iaoiaeeoueny a aeaeaeaiee.

t, no?aiyuainy e ioeth

Oaeei ia?acii,ana yoe ia?aaeienu naycaiu n iiiyoeai i?aaeaea; iii noaei
oeaio?aeueiui iiiyoeai en/eneaiey aaneiia/ii iaeuo.

Ia?aaeienu Caiiia ecaanoiu iai aeaaiaea?y A?enoioaeth,eioi?ue i?eaae eo
a naiae “Oeceea”, /oiau iiaeaa?aiooue e?eoeea. Ii ?acee/aao
aaneiia/iinoue ioiineoaeueii neiaeaiey e aaneiia/iinoue ioiineoaeueii
aeaeaiey e onoaiaaeeaaao, /oi eiioeiooi aaneiia/ii aeaeei. A?aiy oiaea
aaneiia/ii aeaeeii, e a eiia/iue eioa?aae a?aiaie iiaeii i?ieoe
aaneiia/ii aeaeeiia ?annoiyiea. Ia?aaeien “No?aea”, eioi?ue “yaeyaony
neaaenoaeai i?aaeiieiaeaiey, /oi a?aiy ninoaaeaii ec iiiaioia”,
noaiiaeony iaeaiui, anee i?eiyoue, /oi a?aiy aaneiia/ii aeaeeii.

Nienie eeoa?aoo?u

1. Oeaeoai A.A. Enoi?ey iaoaiaoeee a ae?aaiinoe e a n?aaeiea aaea.
I.-E.,1932

2. No?iee Ae.ss. E?aoeee i/a?e enoi?ee iaoaiaoeee. I.,Iaoea,1978

3. Aiaiiieia N.A. Aeooaeueiay aaneiia/iinoue. I.-E.,1934

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