Constructivism (philosophy of mathematics)
In the philosophy of mathematics, constructivism asserts that it is necessary to find (or "construct") a mathematical object to prove that it exists. In classical mathematics, one can prove the existence of a mathematical object without "finding" that object explicitly, by assuming its non-existence and then deriving a contradiction from that assumption. Such a proof by contradiction might be called non-constructive, and a constructivist might reject it. The constructive viewpoint involves a verificational interpretation of the existential quantifier, which is at odds with its classical interpretation.
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Academic grading in the United StatesAlgorithm characterizationsAndrey MarkovAndrey Markov Jr.Anne Sjerp TroelstraApartness relationAreas of mathematicsAxiom of choiceAxiom of limitation of sizeBoris Kushner (mathematician)Brouwer fixed-point theoremBrouwer–Heyting–Kolmogorov interpretationBrouwer–Hilbert controversyCalculusCalculus of constructionsCantor's diagonal argumentCategory theoryChoice sequenceChurch's thesis (constructive mathematics)Classical mathematicsComputable numberConstruction of the real numbersConstructive analysisConstructive mathematicsConstructive proofConstructive set theoryConstructivismConstructivism (math)Constructivism (mathematics)Constructivist (math)Constructivist mathematicsControversy over Cantor's theoryCorrado BöhmCriticism of nonstandard analysisDavid HilbertDenotational semanticsDifferential (infinitesimal)Discontinuous linear mapDisjunction and existence propertiesDivya Dwivedi
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Constructivism (philosophy of mathematics)
In the philosophy of mathematics, constructivism asserts that it is necessary to find (or "construct") a mathematical object to prove that it exists. In classical mathematics, one can prove the existence of a mathematical object without "finding" that object explicitly, by assuming its non-existence and then deriving a contradiction from that assumption. Such a proof by contradiction might be called non-constructive, and a constructivist might reject it. The constructive viewpoint involves a verificational interpretation of the existential quantifier, which is at odds with its classical interpretation.
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En filosofía de las matemática ...... de p y ~p, cabe otra salida).
@es
En philosophie des mathématiqu ...... des mathématiques classiques.
@fr
Het constructivisme is een str ...... ten aanzienlijk is verscherpt.
@nl
In the philosophy of mathemati ...... tive viewpoint on mathematics.
@en
Konstruktivism avser inom mate ...... företrädare för inriktningen.
@sv
Na filosofia da matemática, o ...... vista objetivo em matemática.
@pt
Nella filosofia della matemati ...... oneoggettiva della matematica.
@it
Конструктивна математика — абс ...... ьтати — конструктивні об'єкти.
@uk
Конструктивная математика — аб ...... оветский учёный Андрей Марков.
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在数学哲学中，构成主义或构造主义认为要证明一个数学对象存在就 ...... 主观活动。构成主义不这样强调，并和对数学的客观看法保持一致。
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En filosofía de las matemática ...... enomina platonismo matemático.
@es
En philosophie des mathématiqu ...... à une construction de l'objet.
@fr
Het constructivisme is een str ...... is de , ook wel RUSS genoemd.)
@nl
In the philosophy of mathemati ...... its classical interpretation.
@en
Konstruktivism avser inom mate ...... företrädare för inriktningen.
@sv
Na filosofia da matemática, o ...... a sua interpretação clássica.
@pt
Nella filosofia della matemati ...... è dimostrata la sua esistenza.
@it
Конструктивна математика — абс ...... ьтати — конструктивні об'єкти.
@uk
Конструктивная математика — аб ...... сов и конструктивных объектов.
@ru
在数学哲学中，构成主义或构造主义认为要证明一个数学对象存在就 ...... 主观活动。构成主义不这样强调，并和对数学的客观看法保持一致。
@zh
label
Constructivism (philosophy of mathematics)
@en
Constructivisme (mathématiques)
@fr
Constructivisme (wiskunde)
@nl
Constructivismo (matemáticas)
@es
Construtivismo (matemática)
@pt
Costruttivismo matematico
@it
Konstruktivism (matematik)
@sv
Mathematischer Konstruktivismus
@de
Конструктивная математика
@ru
Конструктивізм (математика)
@uk