Russell chododometsa: mudziwe zofunika, zitsanzo, chiphunzitso

Russell chododometsa ndi awiri modalirana zomveka antinomy.

mitundu iwiri chododometsa Russell

Kwambiri kawirikawiri takambirana mawonekedwe a kutsutsana mu waika maganizo. Ena mwa akonzedwa zikuoneka kuti mamembala okha, ndipo ena - palibe. Achikhalire kukukhala onse ali yokha akonzedwa, kotero zikuwoneka kuti liwu'li likuyimira yokha. Null kapena kanthu Komabe, sitiyenera kukhala membala palokha. Choncho, gulu kukukhala onse, monga ziro sali m'gulu wokha. The chododometsa zimachitika ngati funso ngati ya membala wa yokha. Izi zingatheke ngati ndi pokhapokha ngati izo siziri.

Fomu inanso chododometsa ndi kutsutsana okhudza katundu. Ena katundu, akuoneka kuti amadzitcha, pamene ena. chuma kukhala chuma palokha ndi katundu, pamene chuma zikhale mphaka si. Taganizirani chuma cha kukhala ndi malo amene sikuli kwa iye. ngati agwiritsidwa yokha? Kachiwiri, aliyense wa mfundo akhale otero. chododometsa The dzina lake polemekeza Bertrand Russell (1872-1970), amene anatulukira mu 1901.

nkhani

Oyamba Russell zinachitika pa ntchito yake pa "Mfundo za Masamu". Ngakhale kuti anapeza chododometsa paokha, pali umboni wakuti masamu ena ndi kutukula chiphunzitso akonzedwa, kuphatikizapo Ernst Zermelo ndi David Hilbert, ankadziwa za Baibulo loyamba zotsutsana pamaso pake. Russell Komabe, woyamba amene takambirana mwatsatanetsatane chododometsa ntchito zake lofalitsidwa, titayensa zopanga njira ndi oyamba kumvetsa tanthauzo lake. A mutu wonsewo wa "Mfundo" zoyenera kukambirana nkhaniyi ndi ntchito zoyenera chiphunzitso cha mitundu, amene Russell akufuna monga yankho.

Russell anapeza "chododometsa wa wabodza wa poona Cantor chaikidwa chiphunzitso amene anena kuti mphamvu ya akonzedwa aliyense n'chochepa kuposa ya subsets ake. Osachepera ankalamulira ayenera subsets ochuluka monga pali zinthu mu izo, ngati kagawo wina aliyense mchitidwe wayikidwa uli mchitidwe uwu. Komanso, Cantor anasonyeza kuti chiwerengero cha zinthu sangakhale wolingana ndi chiwerengero cha subsets. Ngati panali nambalayi, akanayenera kuti kulibe Mbali ƒ kuti angasonyeze zinthu pa subsets awo. Pa nthawi yomweyo akhoza anatsimikizira kuti zimenezi n'zosatheka. Zinthu zina akhoza amalembedwa ntchito ƒ subsets okhala iwo, pamene ena ayi.

Taganizirani kagawo wa zinthu zimene si za mafano awo, amene amasonyeza ƒ. Ndi pachokha ndi kagawo wa zinthu, choncho, ntchito ƒ angasonyeze pa mchitidwe mu ulamuliro wa. vuto ndi funso n'lakuti ngati chinthu ichi wa kagawo imene amasonyeza ƒ. Izi zimatheka ngati sikuli. Russell chododometsa Tingaone chitsanzo cha mzere womwewo mfundo okha m'Chingelezi chosavuta. Kodi zambiri - likulowa kapena subsets wa Anatipatsa? Zingatanthauze kuti pazikhala waika zambiri, monga subsets onse likulowa okha. Koma ngati Lingaliro Lovomerezeka Cantor ndi zoona, ndiye payenera kukhala subsets. Russell wosasamala chabe kusonyeza waika okha ndi ntchito njira kantoriansky kuganizira ya zinthu izi zonse, kunja kwa akonzedwa limene anasonyeza. Kuonetsa Russell wobwezera ya waika zonse sanali.

zolakwa Frege

"The chododometsa wa wabodza" kunathandiza kwambiri pa chitukuko mbiri ndi chiphunzitso cha waika. Iye anasonyeza kuti mfundo akonzedwa chilengedwe kwambiri mabvuto. Iye ankakayikira chiphunzitso kuti aliyense chikhalidwe amawamasulira kapena mkhalidwe kukhulupirira kuti kuli kuchuluka zokhazo zimene kukwaniritsa chikhalidwe ichi. Yankho chododometsa za katundu - ndi kutambasuka achilengedwe waika Baibulo - anayamba kukayikira kwambiri ngati n'zotheka kukanganira za cholinga kuli chuma kapena kuvomereza chilengedwe aliyense anatsimikiza ndi chikhalidwe, kapena mkhalidwe.

Posachedwa zotsutsana ndi mavuto mu ntchito ya logicians anawapeza, nzeru ena ndi masamu amene anapanga mfundo zofanana. Mu 1902, Russell anapeza kuti zosinthika wa chododometsa ndi tingasonyezere dongosolo tawerenga, anayamba mu Volume I ya "Madziko a masamu" Gottlob Frege, mmodzi mwa ntchito yaikulu pa mfundo za XIX mochedwa - oyambirira XX atumwi. Mu nzeru za Frege ambiri anamvetsa ngati "kutambasuka" kapena "phindu osiyanasiyana" lingaliro. mfundo ndi pafupi ndi anthu a correlates. Amayenera zikhalepo kwa chikhalidwe iliyonse kapena mkhalidwe. Choncho, pali mfundo akonzedwa, omwe si kugwa pansi mfundo zake liwulo. Palinso kalasi chimafotokozera lingaliro ili, ndipo phunziro kwa liwulo mfundo zake pokhapokha ngati izo siziri.

Russell analemba kuti Frege za mkangano June 1902 Makalata ndi limodzi mwa chidwi kwambiri ndi ikunenedwa mu mbiriyakale maganizo. Frege anawazindikira zotsatirapo zoopsa za chododometsa lapansi. Iye anati Komabe, Baibulo pa mlanduwo yokhudza katundu nthanthi wake kuthetsa kusiyanitsa malingaliro a misinkhu.

Maganizo Frege zinadziŵa monga kusintha kwa zokangana za ntchito kwa WOONA. Zikhulupiriro mlingo woyamba kudzitengera mfundo zinthu malingaliro mlingo wachiwiri monga mikangano kuti ntchito izi, ndi zina zotero. Choncho, lingaliro akhoza konse wokha ngati mkangano, ndi chododometsa mawu a katundu sangakhoze anakonza. Komabe akanema, Kukuza kapena mfundo Frege anamvetsa amanena za yemweyo zomveka mtundu ngati kuti zinthu zina zonse. Kenako aliyense akonzedwa pali funso ngati imagwera pa mfundo liwulo.

Pamene Frege, Russell analandira kalata yoyamba, buku lachiwiri la "Madziko a masamu" kale anamaliza kulisindikiza. Anakakamizika mofulumira kukonzekera ntchito kuti amapereka yankho kwa chododometsa a Russell. Zitsanzo Frege zili nambala ya njira zothetsera mavuto. Koma iye anazindikira kufooketsa mfundo abstraction akonzedwa mu dongosolo ndi mfundo zomveka.

Pachiyambi, kunali kotheka kunena kuti chinthu limabweretsa akonzedwa ngati ndi pokhapokha ngati imagwera mkati zosiyana, tanthauzo. Dongosolo ndikusinthidwa pomaliza kuti chinthu limabweretsa akonzedwa ngati ndi pokhapokha ngati imagwera mkati lingaliro la liwulo ndi kuchuluka, koma anapereka funso. Russell chododometsa kutero.

Yankho Komabe, si kwathunthu okhutitsidwa ndi Frege. Ndipo uyu anali chifukwa. Patapita zaka zingapo, zovuta kwambiri mtundu wa kutsutsana wapezeka kwa dongosolo yantchito. Koma ngakhale izi zisanachitike chinachitika, Frege anasiya kaye maganizo anga ndipo zikuoneka kuti afika pozindikira kuti ulaliki wake anali chabe unworkable, ndi kuti mfundo mudzachita popanda kukukhala ndi.

Komabe ena akhala akufuna, njira zina zothetsera kusamvana ndi zambiri bwino. Izi zafotokozedwa pansipa.

Chiphunzitso cha mitundu

Iwo anali taonera kuti Frege anali munthu amene chokwanira kwa paradoxes chiphunzitso akonzedwa mu Baibulo anakonza kwa katundu. Yankho Frege anali yoyamba njira kwambiri kawirikawiri anakambirana mawonekedwe chododometsa. Bukuli lili ndi mfundo yakuti katundu imvera osiyanasiyana ndi zimene mtundu wa chuma si mofanana zinthu zimene amanena.

Choncho, ngakhale funso n'lakuti, ngati katundu ndi ntchito yokha. chilankhulo zomveka, lomwe limasiyanitsa zinthu zoterozo ufumu, kugwiritsa ntchito chiphunzitso cha mitundu. Ngakhale kale ntchito ndi Frege, nthawi yoyamba yomwe iyo kwathunthu anafotokoza ndi m'Malemba Russell mu alumikiza kwa "Mfundo". Chiphunzitso cha mitundu adakwaniritsidwa kuposa amasiyana ndi milingo Frege. Iye nawo katundu osati osiyanasiyana maganizo, koma anatipatsa. kutayipa chiphunzitso kuthetsa kutsutsana mu chododometsa a Russell motere.

Pofuna kukhala philosophically chokwanira, kukhazikitsidwa ndi chiphunzitso cha mitundu ya katundu amafuna chitukuko cha chiphunzitso cha chikhalidwe cha katundu kuti akhoza kufotokoza chifukwa iwo sangathe ntchito okha. Koyamba, n'zomveka kuti mkhalidwe chuma chawo. Chuma cha kudzikonda dzina, zingatanthauze, komanso ndi kudzikonda abwino. katundu zikuoneka kukhala zabwino zosangalatsa. Mu njira yomweyo, zikuoneka, zikuoneka onyenga kunena kuti chuma cha kukhala mphaka ndi mphaka.

Komabe, anthu anzeru osiyanasiyana wolungama nsoka wa mitundu yosiyanasiyana. Russell anapatsa mafotokozedwe osiyanasiyana panthawi zosiyanasiyana mu ntchito yake. Gawo limeneli ndi chowaloleza kwa kulekana kwa mfundo zosiyanasiyana za misinkhu Frege amachokera chiphunzitso chakuti mfundo unsaturated. Mfundo monga ntchito, kwenikweni, ndi chosakwanira. Kupereka phindu, ayenera kukangana. Inu simungakhoze lingaliro limodzi chabe kwa mkhalidwe mfundo yofanana, chifukwa amafuna mkangano ake. Mwachitsanzo, ngakhale kuli kotheka kuti atenge muzu lalikulu la muzu lalikulu angapo, inu simungakhoze basi ntchito sikweya muzu ntchito ku muzu ntchito lalikulu ndi kupeza chifukwa.

Za katundu conservatism

njira china ndi chododometsa katundu negation katundu kuli m'mikhalidwe iliyonse, kapena mkhalidwe wokongola. Kumene, ngati munthu eschews katundu akamabadwa wa zinthu zonse cholinga ndi ufulu wodzilamulira wonse ngati ife nominalism chododometsa zikhoza kupewedwa kwathunthu.

Komabe, kuthetsa antinomy suyenera kukhala choncho kwambiri. Zomveka kuti apamwamba machitidwe anayamba Frege ndi Russell, muli zimene amatchedwa mfundo cilamulo, chimene aliyense lotseguka mitunduyi kaya zovuta alipo monga gawo la chuma kapena lingaliro mwachitsanzo, okhawo zinthu zimene zikugwirizana ndi mfundo. Mfundozo malingaliro a aliyense akonzedwa kuti mwina zinthu kapena predicates, ziribe kanthu momwe zovuta iwo anali.

Komabe, kunali kotheka kutenga zambiri okhwima metaphysics katundu, kupereka ufulu cholinga kuli katundu yosavuta, kuphatikizapo Mwachitsanzo, monga mtundu wofiira, kulimba mtima, chifundo ndi zina zotero. D. Mungathe ngakhale katundu awa amagwiritsa ntchito, monga kukoma mungathe kukhala mtundu.

Ndipo udindo chimodzimodzi zotsatira zovuta akhoza adakana, mwachitsanzo, ngati "katundu" ngati ndi ziwiri-mitu kukhala olembedwa pansi madzi ndi zina zotero. D. Pankhaniyi, palibe anakonzeratu chikhalidwe si kukumana chuma, kuwamva monga payokha amafotokozera, amene ali katundu zake zilipo. Choncho angatsutse kuli katundu yosavuta akhale chuma kuti, si ntchito ndi kudzikonda ndi kupewa chododometsa kutsatira kwambiri ndiwofatsa akamabadwa katundu.

Russell chododometsa: yothetsera

Pamwamba inafotokoza kuti pa mapeto a moyo wake Frege kwathunthu anasiya mfundo kukukhala. Izi, kumene, munthu yothetsera antinomy mu mawonekedwe kukukhala: losavuta kukana kukhalako kwa zinthu monga lonse. Komanso, pali zosankha zina otchuka, ndizosowa amene pansipa.

Chiphunzitso cha osiyanasiyana

Monga tanena kale, Russell kuimba chiphunzitso kokwanira kwambiri a mitundu, amene adzagwirizana katundu osati kapena mfundo kwa mitundu yosiyanasiyana, koma anatipatsa. Russell takumananso anakhala pa kuchuluka mayunitsi osiyana, ndi kuchuluka kukukhala a zinthu zosiyana, etc. The waika zinthu ankaziona kuti ndi kuchuluka kukukhala - .. amakhala. A ambiri sanamvepo kukoma mtundu, wakulolani kukhala monga chiwalo cha yokha. Choncho palibe ya waika zonse si mamembala zake, chifukwa akonzedwa mafunso ngati ndi monga chiwalo, ndi palokha mtundu kuphwanya. Kachiwiri, nkhani apa ndi kufotokoza likulowa metaphysics kufotokoza maziko nthanthi ya kugawikana mu mitundu.

stratification

Mu 1937, V. V. Kuayn ali anapereka njira ina, mofananamo ku chiphunzitso cha mitundu. zokhuza muli.

Kupatuka waika amafotokozera ndi ena. Anapanga kuti kopanda kupeza kuchuluka zonse sizolondola kapena phindu. Akanema zitha anapereka pamene liwulo zikhalidwe si mtundu kuphwanya. Choncho, Quine, mawu akuti "× si membala wa ×" Ndi mfundo zogwira sizikutanthauza kuti kuli kuika zinthu zonse × wokhutiritsa chikhalidwe ichi.

Mu dongosolo ili akonzedwa alipo ena lotseguka chilinganizo A ngati ndipo kokha ngati stratified, T. E. Ngati zosintha amapatsidwa integers zabwino ngati kuti aliyense yatsoka khalidwe la kuchuluka kwa yapitayi izo variable akapatsidwa ntchito wagawo kakang'ono kuposa variable ndi, kumutsanzira. Izi midadada Russell chododometsa, popeza njira ntchito kudziwa kuika vuto, pali chimodzimodzi pambuyo pa variable umembala chizindikiro kupangitsa unstratified.

Koma koma kuti aone ngati dongosolo chifukwa, zomwe Quine otchedwa "New Madziko maganizo masamu" Musamasinthesinthe.

kukanidwa

Njira zosiyana atengedwa mu chiphunzitso cha Zermelo - Fraenkel (ZF). Apanso, anapereka malire pa kuli waika. M'malo mwake, tiyandikire "pamwamba-pansi" kwa Russell ndi Frege, amene poyamba ankaganiza kuti mfundo zonse, katundu, kapena zinthu kamasonyeza kuli chifukwa cha zinthu zonse ndi chuma ichi kapena kukumana chikhalidwe choterocho, mu ZF-chiphunzitso, chirichonse kumayamba "kuchokera pansi mmwamba."

zinthu aliyense kuika kanthu ndi kupanga akonzedwa. Choncho, mosiyana ndi machitidwe kale ndi Russell Frege ZOKONZEKERA sikuli kwa akonzedwa chilengedwe zomwe zikuphatikizapo zinthu zonse ndipo ngakhale waika zonse. ZF salola okhwima pa kuli waika. Angathe kukhala okhawo amene mosapita postulated kapena kumene anakonza kudzera mwa njira iterative ndi zina zotero. D.

Kenako, mmalo mwa mfundo abstraction zilizonse akonzedwa umene umati chinthu makamaka m'gulu akonzedwa ngati ndi pokhapokha ngati likukwaniritsa zinthu kulekana mfundo ntchito DF, kupatukana kapena "kusanja". M'malo moganiza kuli kuika zinthu zonse zimene zili mosachotsera kukwaniritsa chikhalidwe ena, aliyense akonzedwa alipo Aussonderung limasonyeza kuti kuli kagawo zinthu zonse mwa kuika choyambirira chimene imakwaniritsa chikhalidwe.

Pamenepo adadzanso mfundo abstraction: ngati kuika A alipo, ndiye, kuti × onse A, × wa kagawo A, omwe amakwaniritsa chikhalidwe ngati ndipo ngati × amakwaniritsa chikhalidwe C. Njira imeneyi watsimikiza za chododometsa Russell, kuyambira sitingayendere kuganiza ndiko kuti, ya waika zonse sakhala mamembala a iwo okha.

Kukhala kwambiri ndi mipukutu, mukhoza kusankha kapena muchigawane mu akanema, amene mwa iwo okha, ndi anthu amene sali zimenezi, koma popeza palibe akonzedwa chilengedwe ife samangika ya waika zonse. Popanda kuganiza vuto kumasiyanitsa Russell kutsutsana sizingakhoze kutsimikiziridwa.

njira zina

Komanso, pakhala yophunzitsa wotsatira kapena zosintha njira izi, monga foloko-mtundu chiphunzitso cha "Mfundo za Masamu" dongosolo kuwonjezeka "masamu mfundo" Quine, komanso zikuchitika posachedwapa mchiphunzitso cha akanema, anapanga Bernays, Gödel ndi Von Neumann. Funso ngati yankho kwa chododometsa insoluble Bertrand Russell anapeza, akadali ndi nkhani ya mtsutso.