직관주의

직관주의(直觀主義, 영어: Intuitionism)란, 수학의 개념들은 인간의 건설적 사고 활동의 결과일 뿐, 객관적인 실재(objective reality)에 존재하는 기본 원리들이 발견되는 것으로 볼 수 없다고 접근하는 입장이다. 이는 곧 수학과 논리학의 기초가 수학자의 직관에서 유래되었다고 주장하는 입장으로, 수학의 개념들은 그 체계 내부에서는 영원히 참이지만 이것을 실제 세계에 반드시 적용할 수 있는 것은 아니라고 주장하는 것이다.

근대에 칸토어의 비직관적인 무한집합론이 주장되자 크로네커와 푸앵카레 등이 이에 대항하는 주장을 폄으로써 초기 형태의 직관주의가 대두되기 시작하였다. 이후 라위트전 브라우어르는, 수학적 개념들이 그저 수학자들의 사고의 산물일 뿐이며 그 존재는 그 구성에 의해 보여져야 한다는 입장에서, 무한집합의 존재의 증명에 있어서 '그것이 존재하지 않는 경우 모순이 발생하므로 그 존재가 증명된다'는 귀류법적 증명방법을 부정하였으며, 이에 따라 무한집합에 있어서 배중률, 곧 어떠한 명제는 참이나 거짓 둘 중 하나이어야 한다는 추론법칙을 버릴 필요가 있다며, 수학의 무모순성을 제창하며 형식주의를 고수하던 힐베르트와의 사이에 논쟁을 일으키기도 했다. 이후 브라우어의 주장은 아런트 헤이팅 등에 의해 정비되어 고전논리의 배중률을 인정하지 않는 직관논리로써 형식화되었고, 수학적 구성주의와도 많은 관련성, 유사성을 보이고 있다.

브라우어르가 현대적 직관주의를 확립하였으므로, 크로네커나 푸앵카레 등의 입장은 전직관주의 혹은 구직관주의(preintuitionism), 그리고 브라우어르 및 그 이후의 직관주의적 입장은 신직관주의(neointuitionism)이라고 구분되어 불리기도 한다.

같이 보기

Portal icon수학 포털

Read other articles:

Antillattus placidus

Artikel ini sebatang kara, artinya tidak ada artikel lain yang memiliki pranala balik ke halaman ini.Bantulah menambah pranala ke artikel ini dari artikel yang berhubungan atau coba peralatan pencari pranala.Tag ini diberikan pada Oktober 2016. Antillattus placidus Klasifikasi ilmiah Kerajaan: Animalia Filum: Arthropoda Kelas: Arachnida Ordo: Araneae Famili: Salticidae Genus: Antillattus Spesies: Antillattus placidus Nama binomial Antillattus placidusBryant, 1943 Antillattus placidus adalah s...

 

Double planet

A binary system where two planetary-mass objects share an orbital axis external to both For a star orbited by two planets, see Double-planet system. See also: Satellite system (astronomy) Visual comparison of the sizes of Earth and the Moon (above right) and Pluto–Charon (below right) In astronomy, a double planet (also binary planet) is a binary satellite system where both objects are planets, or planetary-mass objects, that share an orbital axis external to both planetary bodies. Although...

 

Olbia

OlbiaKomuneComune di OlbiaLokasi Olbia di Provinsi SassariNegaraItaliaWilayahSardiniaProvinsiSassari (SS)FrazioniBerchiddeddu, Murta Maria, Pittulongu, Rudalza-Porto Rotondo, San PantaleoPemerintahan • Wali kotaSettimo NizziLuas • Total376,10 km2 (14,520 sq mi)Populasi (2010) • Total56.231 • Kepadatan1,5/km2 (3,9/sq mi)DemonimOlbiesiZona waktuUTC+1 (CET) • Musim panas (DST)UTC+2 (CEST)Kode pos07026Kode area t...

Homo antecessor

Archaic human species from 1 million years ago Homo antecessorTemporal range: Early Pleistocene, 1.2–0.77 Ma PreꞒ Ꞓ O S D C P T J K Pg N ↓ The Boy of Gran Dolina fossilsATD6-15 (frontal bone)ATD6-69 (maxilla)Museo Arqueológico Nacional, Madrid Scientific classification Domain: Eukaryota Kingdom: Animalia Phylum: Chordata Class: Mammalia Order: Primates Suborder: Haplorhini Infraorder: Simiiformes Family: Hominidae Subfamily: Homininae Tribe: Hominini Genus: Homo Species: ...

 

Tony Gabriel

Canadian gridiron football player (born 1948) Tony GabrielNo. 77Canada's Sports Hall of Fame Induction, November 10, 2010Born: (1948-12-11) December 11, 1948 (age 75)Burlington, Ontario, CanadaCareer informationCFL statusNationalPosition(s)TEHeight6 ft 4 in (193 cm)Weight210 lb (95 kg)CollegeSyracuseHigh schoolBurlington CentralCareer historyAs player1971–1974Hamilton Tiger-Cats1975–1981Ottawa Rough Riders Career highlights and awards...

 

1964 Savage Mountain B-52 crash

Nuclear bomber accident Savage Mountain B-52 crashA Boeing B-52D, similar to the accident aircraftAccidentDate13 January 1964 (1964-01-13)SummaryStructural failureSiteSavage Mountain, Garrett County (near Frostburg, Maryland) 39°33′55″N 79°04′33″W / 39.565278°N 79.075833°W / 39.565278; -79.075833 (1964 Savage Mountain B-52 crash)AircraftAircraft typeBoeing B-52D StratofortressOperator484th Bombardment Wing, Heavy (SAC, United Sta...

Tom and Jerry (Van Beuren)

1930's animated characters created by the Van Beuren Studio For the later MGM cartoon cat and mouse duo, see Tom and Jerry. This article needs additional citations for verification. Please help improve this article by adding citations to reliable sources. Unsourced material may be challenged and removed.Find sources: Tom and Jerry Van Beuren – news · newspapers · books · scholar · JSTOR (April 2021) (Learn how and when to remove this message) Fil...

 

Gros Morne National Park

National Park on the west coast of Newfoundland For other uses, see Gros Morne (disambiguation). Gros Morne National ParkIUCN category II (national park)Western Brook Pond in Gros Morne National ParkLocation of Gros Morne National Park in CanadaShow map of CanadaLocation of Gros Morne National Park in NewfoundlandShow map of NewfoundlandLocationRocky Harbour, Newfoundland and Labrador, CanadaCoordinates49°41′22″N 57°44′17″W / 49.68944°N 57.73806°W / 49.6894...

 

Dover Castle

Medieval castle in Dover, Kent, England Dover CastleDover, Kent, England Aerial panorama of the castleDover CastleCoordinates51°07′47″N 1°19′17″E / 51.1297°N 1.3214°E / 51.1297; 1.3214TypeNorman castleSite informationOwnerEnglish HeritageConditionIntactSite historyBuilt12th centuryBuilt byHenry IIEventsFirst Barons' War vteFirst Barons' War1215–1217 Dover Castle Windsor Castle Hertford Lincoln Rochester Sandwich Dover Castle is a medieval castle in D...

هنود

هنودمعلومات عامةنسبة التسمية الهند التعداد الكليالتعداد قرابة 1.21 مليار[1][2]تعداد الهند عام 2011ق. 1.32 مليار[3]تقديرات عام 2017ق. 30.8 مليون[4]مناطق الوجود المميزةبلد الأصل الهند البلد الهند  الهند نيبال 4,000,000[5] الولايات المتحدة 3,982,398[6] الإمار...

 

1900 Florida gubernatorial election

For related races, see 1900 United States gubernatorial elections. 1900 Florida gubernatorial election ← 1896 November 6, 1900 1904 →   Nominee William Sherman Jennings Matthew B. MacFarlane Party Democratic Republican Popular vote 29,251 6,238 Percentage 80.98% 17.27% County Results Congressional District Result Jennings  50–60%  60–70%  70–80%  80–90%  >90% Governor before election William D. ...

 

哈萨克斯坦总统

此条目序言章节没有充分总结全文内容要点。 (2019年3月21日)请考虑扩充序言，清晰概述条目所有重點。请在条目的讨论页讨论此问题。 哈萨克斯坦總統哈薩克總統旗現任Қасым-Жомарт Кемелұлы Тоқаев卡瑟姆若马尔特·托卡耶夫自2019年3月20日在任任期7年首任努尔苏丹·纳扎尔巴耶夫设立1990年4月24日（哈薩克蘇維埃社會主義共和國總統） 哈萨克斯坦 哈萨克斯坦政府...

البهجة الموعودة (رواية)

هذه المقالة تحتاج للمزيد من الوصلات للمقالات الأخرى للمساعدة في ترابط مقالات الموسوعة. فضلًا ساعد في تحسين هذه المقالة بإضافة وصلات إلى المقالات المتعلقة بها الموجودة في النص الحالي. (يوليو 2021) البهجة الموعودة تعديل مصدري - تعديل   البهجة الموعودة (بالإنجليزية: The Promise of Jo...

 

Bath salts (drug)

Recreational drug often superficially resembling true bath salts This article may lack focus or may be about more than one topic. Please help improve this article, possibly by splitting the article and/or by introducing a disambiguation page, or discuss this issue on the talk page. (August 2018) Bath salts (also called psychoactive bath salts, PABS[1][2]) are a group of recreational designer drugs.[3][4] The name derives from instances in which the drugs were d...

 

شلن صومالي

شلن صوماليمعلومات عامةالبلد  الصومال تاريخ = 1962تاريخ الإصدار 11 ديسمبر 1974 عوض شلن شرق افريقي رمز العملة Sh.So. رمز الأيزو 4217 SOSالمصرف المركزي البنك المركزي الصوماليسعر الصرف 0٫001467 يورو (28 أغسطس 2020) تعديل - تعديل مصدري - تعديل ويكي بيانات الشلن الصومالي، هو العملة الرسمية للصو�...

Maria Dermoût

Maria Dermoût pada tahun 1907 Maria Dermoût (15 Juni 1888 – 27 Juni 1952) adalah seorang penulis Indo paruh pertama abad ke-20 yang menulis dalam bahasa Belanda. Dermoût diakui sebagai salah seorang tokoh paling terkemuka dalam sastra Belanda dan sastra Hindia Belanda. Dalam terbitannya tertanggal Desember 1958, majalah Amerika Time memuji karyanya De Dienduizend Dingen (kesepuluh ribu hal, 1955), yang diterjemahkan ke bahasa Inggeris dengan judul The Ten Thousand Things, s...

 

Aardman Animations

British animation studio Aardman Animations LimitedLogo used since 2022FormerlyOffshelm Limited (August–November 1986)[1]Aards Co. Limited(The) (1986–1987)[1]Company typePrivateIndustryAnimationFounded1972; 52 years ago (1972)FoundersPeter LordDavid SproxtonHeadquartersGas Ferry Road, Bristol, EnglandNumber of locations5Key peoplePeter LordNick ParkDavid SproxtonDivisionsAardman Features LimitedAardman DigitalAardman CommercialsAardman BroadcastAardman In...

 

Canal de l'Eure

Canal de l'EureCanal Louis XIV Le canal de l'Eure à Maintenon (Aqueduc de Maintenon). Géographie Pays France Coordonnées 48° 29′ 16″ N, 1° 07′ 59″ E Début Pontgouin (département d'Eure-et-Loir) Fin Étang de la Tour (département des Yvelines) Traverse Saint-Arnoult-des-Bois, Fontaine-la-Guyon, Pontgouin, Maintenon Caractéristiques Statut actuel Radié Longueur 80 km Histoire Année début travaux 1685 Année d'ouverture resté inachevé Com...

コスモポリタン製菓

有限会社コスモポリタン製菓The Cosmopolitan Confectionery 神戸本店種類 有限会社市場情報 非上場本社所在地 日本〒650-0046神戸市中央区港島中町7丁目7-3設立 1969年業種 食料品事業内容 洋菓子の製造・販売代表者 代表取締役 ヴァレンティン・ヴァレンティノヴィチ・モロゾフ（閉業時）資本金 500万円売上高 15億円（2001年度）従業員数 67名（2002年4月）関係する人物 ヴァレン�...

 

Luca Koleosho

Footballer (born 2004) Luca Koleosho Koleosho with Espanyol in 2022Personal informationFull name Luca Warrick Daeovie Koleosho[1]Date of birth (2004-09-15) 15 September 2004 (age 19)[1]Place of birth Norwalk, Connecticut, U.S.Height 1.75 m (5 ft 9 in)[1]Position(s) Left wingerTeam informationCurrent team BurnleyNumber 30Youth career2011–2012 Trumbull United2012–2016 Manhattan Kickers2016–2020 Reus2020–2022 EspanyolSenior career*Years Team Ap...