intuitionism
E503512
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.
All labels observed (3)
| Label | Occurrences |
|---|---|
| intuitionistic logic | 6 |
| Moorean intuitionism | 1 |
| intuitionism canonical | 1 |
How this entity was disambiguated
This entity first appeared as the object of triple T5211840 — resolving that mention is where its identity was fixed. The disambiguator weighed these candidate entities and picked the highlighted one (or “None”, minting a new entity). This is how homonymy is resolved: the same surface form can point to different entities.
NED1
Entity disambiguation (via context triple)
gpt-5-mini-2025-08-07
Target entity: intuitionism Context triple: [Philosophy of Mathematics and Natural Science, influencedBy, intuitionism]
-
A.
Elements of Intuitionism
Elements of Intuitionism is a foundational philosophical and logical treatise by Michael Dummett that systematically develops and defends intuitionistic logic and mathematics.
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B.
Brouwer–Heyting–Kolmogorov interpretation
The Brouwer–Heyting–Kolmogorov interpretation is a foundational explanation of intuitionistic logic that interprets logical connectives and proofs in terms of explicit constructions and algorithms rather than classical truth values.
-
C.
Dialectica
Dialectica is a theological and philosophical treatise by John of Damascus that systematically presents and defends Christian doctrine using Aristotelian logic and categories.
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D.
Hilbert–Brouwer controversy
The Hilbert–Brouwer controversy was an early 20th-century foundational dispute in mathematics between David Hilbert’s formalism and L.E.J. Brouwer’s intuitionism over the nature of mathematical truth and proof.
-
E.
Logik
Logik is a foundational work on formal logic by German philosopher and mathematician Gottlob Frege, contributing significantly to the development of modern logic and the philosophy of language.
- F. None of above. chosen
- G. Unsure - the case is ambiguous/there is not enough information to decide.
NED2
Entity disambiguation (via description)
gpt-5-mini-2025-08-07
Target entity: intuitionism Target entity description: 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.
-
A.
Elements of Intuitionism
Elements of Intuitionism is a foundational philosophical and logical treatise by Michael Dummett that systematically develops and defends intuitionistic logic and mathematics.
-
B.
Brouwer–Heyting–Kolmogorov interpretation
The Brouwer–Heyting–Kolmogorov interpretation is a foundational explanation of intuitionistic logic that interprets logical connectives and proofs in terms of explicit constructions and algorithms rather than classical truth values.
-
C.
Dialectica
Dialectica is a theological and philosophical treatise by John of Damascus that systematically presents and defends Christian doctrine using Aristotelian logic and categories.
-
D.
Hilbert–Brouwer controversy
The Hilbert–Brouwer controversy was an early 20th-century foundational dispute in mathematics between David Hilbert’s formalism and L.E.J. Brouwer’s intuitionism over the nature of mathematical truth and proof.
-
E.
Logik
Logik is a foundational work on formal logic by German philosopher and mathematician Gottlob Frege, contributing significantly to the development of modern logic and the philosophy of language.
- F. None of above. chosen
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
ⓘ
Brouwer–Heyting–Kolmogorov interpretation ⓘ Heyting arithmetic ⓘ intuitionistic logic ⓘ
linked to:
intuitionism
|
| 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
ⓘ
classical mathematicians ⓘ |
| denies | law of excluded middle for arbitrary infinite totalities ⓘ |
| developedBy |
L. E. J. Brouwer
ⓘ
linked to:
Luitzen Egbertus Jan Brouwer
|
| developedIn | early 20th century ⓘ |
| emphasizes |
constructive proofs
ⓘ
mathematics as a mental activity ⓘ |
| foundedBy |
L. E. J. Brouwer
ⓘ
linked to:
Luitzen Egbertus Jan Brouwer
|
| 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
ⓘ
constructive mathematics ⓘ intuitionistic logic ⓘ topos theory ⓘ
linked to:
Grothendieck toposes
|
| 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
ⓘ
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 ⓘ |
How these facts were elicited
The pipeline generated the facts above by prompting gpt-5.1 with this entity's name + description and the instruction below.
Instruction
You are a knowledge base construction expert. Given a subject entity and a description of it, return factual statements that you know for the subject as a JSON list of dictionaries(triples), where keys must be "subject", "predicate" and "object". The number of facts may be very high, between 25 to 50 or more, for very popular subjects. For less popular subjects, the number of facts can be very low, like 5 or 10. # Requirements - If you don't know the subject at all, return an empty list. - If the subject is not a named entity, return an empty list. - Include at least one triple where predicate is "instanceOf". - Do not get too wordy. - Separate several objects into multiple triples with one object.
Input
Subject: intuitionism Description of subject: 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.
Referenced by (8)
Full triples — surface form annotated when it differs from this entity's canonical label.
linked to: intuitionism
linked to: intuitionism
linked to: intuitionism
linked to: intuitionism
linked to: intuitionism
linked to: intuitionism
linked to: intuitionism