intuitionism

/ˌɪntuˈɪʃənɪzəm/ noun

An approach to mathematics/logic which avoids proof by contradiction, and which requires that, in order to prove that something exists, one must construct it.

Word Origin Intuitionism is built from Latin in- 'in, upon' and tueri 'to look at, watch over.' Intuition is literally 'looking upon' something inwardly, a direct insight. The -ism makes it a doctrine. The same root tueri gives us tutor (one who watches over), tuition (guardianship, then teaching), and tutelage. The PIE root *tew- meant to observe. So intuitionism is the philosophy that knowledge comes from inner looking.

noun An approach to mathematics/logic which avoids proof by contradiction, and which requires that, in order to prove that something exists, one must construct it. countable

Intuitionism rejects proof by contradiction, requiring constructive methods for mathematical existence proofs.

(名词) 直觉主义 【直觉主义(数学/逻辑中拒斥反证法,要求通过构造证明存在性的方法)】

直觉主义拒绝使用反证法,要求用构造性方法进行数学存在性证明。

(sustantivo) intuicionismo [Un enfoque de las matemáticas/lógica que evita la prueba por contradicción, y que requiere que, para demostrar que algo existe, se debe construir.]

El intuicionismo rechaza la prueba por contradicción, requiriendo métodos constructivos para las pruebas de existencia matemática.

(nom) intuitionnisme [Courant en mathématiques et en logique qui rejette la preuve par contradiction et exige, pour démontrer l'existence d'un objet, d'en fournir une construction explicite.]

L'**intuitionism** exige des méthodes constructives pour les preuves d'existence en mathématiques, à la différence de l'approche classique.

(Substantiv) Intuitionismus [Eine philosophische Strömung in der Mathematik und Logik, die Beweise durch Widerspruch ablehnt und fordert, dass Existenzbehauptungen konstruktiv bewiesen werden müssen.]

**Intuitionism** lehnt Widerspruchsbeweise ab und verlangt konstruktive Methoden für mathematische Existenzaussagen.

(名詞) 背理法による証明を避け、あるものの存在を証明するためにはそれを構成しなければならないとする、数学・論理へのアプローチ。

直観主義は背理法による証明を退け、数学的な存在証明には構成的手法が必要だとする。

(substantivo) intuicionismo [Uma abordagem à matemática/lógica que evita a prova por contradição e que exige que, para provar que algo existe, é necessário construí-lo.]

O intuicionismo rejeita a prova por contradição, exigindo métodos construtivos para provas de existência matemática.

Word parts: in + tuit + ion + ism

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