intuitionism

E503512

constructivist philosophy of mathematics mathematical philosophy philosophy of mathematics

Intuitionism is a philosophy of mathematics that views mathematical objects as mental constructions and rejects the unrestricted use of classical logic, especially the law of excluded middle.

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Observed surface forms (2)

Surface form	Occurrences
intuitionistic logic	2
Moorean intuitionism	1

Statements (47)

Predicate	Object
instanceOf	constructivist philosophy of mathematics ⓘ mathematical philosophy ⓘ philosophy of mathematics ⓘ
accepts	finite combinatorial reasoning ⓘ proofs that provide explicit constructions ⓘ
associatedWith	Brouwerian continuity principle NERFINISHED ⓘ Brouwer–Heyting–Kolmogorov interpretation NERFINISHED ⓘ Heyting arithmetic NERFINISHED ⓘ intuitionistic logic NERFINISHED ⓘ
basedOn	mental construction of mathematical objects ⓘ
centralConcept	construction of mathematical objects in time ⓘ mathematics as free creation of the mind ⓘ
contrastsWith	classical mathematics ⓘ formalism ⓘ logicism ⓘ
criticizedBy	David Hilbert NERFINISHED ⓘ classical mathematicians ⓘ
denies	law of excluded middle for arbitrary infinite totalities ⓘ
developedBy	L. E. J. Brouwer NERFINISHED ⓘ
developedIn	early 20th century ⓘ
emphasizes	constructive proofs ⓘ mathematics as a mental activity ⓘ
foundedBy	L. E. J. Brouwer NERFINISHED ⓘ
holdsThat	a mathematical statement is true only if a construction proving it is known ⓘ mathematical objects do not exist independently of the human mind ⓘ truth is identified with provability ⓘ
influenced	Bishop-style constructive analysis NERFINISHED ⓘ constructive mathematics ⓘ intuitionistic logic ⓘ topos theory NERFINISHED ⓘ
influencedBy	Immanuel Kant ⓘ phenomenology ⓘ
inMathematicsDomain	foundations of mathematics ⓘ mathematical logic ⓘ
inPhilosophyDomain	epistemology of mathematics ⓘ ontology of mathematical objects ⓘ
modifies	classical logical connectives ⓘ
opposes	classical Platonist views of mathematics ⓘ mathematical realism ⓘ
rejects	general validity of the law of excluded middle ⓘ unrestricted use of classical logic ⓘ
relatedTo	Brouwer–Heyting logic NERFINISHED ⓘ constructive type theory ⓘ proof theory ⓘ
supports	rejection of actual infinity in some contexts ⓘ rejection of non-constructive existence proofs ⓘ
uses	intuitionistic logic instead of classical logic ⓘ

Referenced by (4)

Full triples — surface form annotated when it differs from this entity's canonical label.

Philosophy of Mathematics and Natural Science → influencedBy → intuitionism ⓘ

open-question argument → associatedWith → intuitionism ⓘ

this entity surface form: Moorean intuitionism

Gerhard Gentzen → influenced → intuitionism ⓘ

this entity surface form: intuitionistic logic

Truth and Other Enigmas → influencedBy → intuitionism ⓘ

this entity surface form: intuitionistic logic