Hilbert’s program
E41775
Hilbert’s program was an influential early-20th-century initiative in the foundations of mathematics that sought to formalize all of mathematics and prove its consistency using finitistic methods.
All labels observed (7)
How this entity was disambiguated
This entity first appeared as the object of triple T326969 — 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: Hilbert’s program Context triple: [David Hilbert, notableWork, Hilbert’s program]
-
A.
On Computable Numbers with an Application to the Entscheidungsproblem
"On Computable Numbers, with an Application to the Entscheidungsproblem" is Alan Turing’s landmark 1936 paper that introduced the Turing machine model and founded the formal study of computability and the limits of algorithmic decision procedures.
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B.
Frege’s system in "Grundgesetze der Arithmetik"
Frege’s system in "Grundgesetze der Arithmetik" is a foundational logical framework for arithmetic based on second-order logic and Basic Law V, whose inconsistency—revealed by Russell’s paradox—marked a turning point in the development of modern logic and set theory.
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C.
Church–Turing thesis
The Church–Turing thesis is a foundational principle in computability theory stating that any function that can be effectively computed by an algorithm can be computed by a Turing machine (or equivalently by other formal models of computation).
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D.
Principia Mathematica
Principia Mathematica is a landmark three-volume work in mathematical logic and the foundations of mathematics, co-authored by Bertrand Russell and Alfred North Whitehead, which aimed to derive all mathematical truths from a formal system of symbolic logic.
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E.
von Neumann–Bernays–Gödel set theory
Von Neumann–Bernays–Gödel set theory is an axiomatic set theory extending Zermelo–Fraenkel set theory by formally distinguishing between sets and classes, widely used in foundational studies of mathematics.
- 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: Hilbert’s program Target entity description: Hilbert’s program was an influential early-20th-century initiative in the foundations of mathematics that sought to formalize all of mathematics and prove its consistency using finitistic methods.
-
A.
On Computable Numbers with an Application to the Entscheidungsproblem
"On Computable Numbers, with an Application to the Entscheidungsproblem" is Alan Turing’s landmark 1936 paper that introduced the Turing machine model and founded the formal study of computability and the limits of algorithmic decision procedures.
-
B.
Frege’s system in "Grundgesetze der Arithmetik"
Frege’s system in "Grundgesetze der Arithmetik" is a foundational logical framework for arithmetic based on second-order logic and Basic Law V, whose inconsistency—revealed by Russell’s paradox—marked a turning point in the development of modern logic and set theory.
-
C.
Church–Turing thesis
The Church–Turing thesis is a foundational principle in computability theory stating that any function that can be effectively computed by an algorithm can be computed by a Turing machine (or equivalently by other formal models of computation).
-
D.
Principia Mathematica
Principia Mathematica is a landmark three-volume work in mathematical logic and the foundations of mathematics, co-authored by Bertrand Russell and Alfred North Whitehead, which aimed to derive all mathematical truths from a formal system of symbolic logic.
-
E.
von Neumann–Bernays–Gödel set theory
Von Neumann–Bernays–Gödel set theory is an axiomatic set theory extending Zermelo–Fraenkel set theory by formally distinguishing between sets and classes, widely used in foundational studies of mathematics.
- F. None of above. chosen
Statements (49)
| Predicate | Object |
|---|---|
| instanceOf |
foundational program in mathematics
ⓘ
philosophy of mathematics position ⓘ research program ⓘ |
| aim |
to formalize all of mathematics
ⓘ
to justify classical mathematics by finitistic means ⓘ to prove the consistency of mathematics ⓘ |
| challengedBy |
Gödel's incompleteness theorems
ⓘ
surface form:
Gödel’s incompleteness theorems
Kurt Gödel ⓘ |
| coreConcept |
consistency proofs
ⓘ
finitism ⓘ formalization of mathematical theories ⓘ |
| countryOfOrigin | Germany ⓘ |
| field |
foundations of mathematics
ⓘ
mathematical logic ⓘ philosophy of mathematics ⓘ proof theory ⓘ |
| hasPart |
development of formal systems for analysis
ⓘ
development of formal systems for arithmetic ⓘ restriction to finitary reasoning in metamathematics ⓘ search for consistency proofs ⓘ |
| historicalEvent | Hilbert–Brouwer controversy ⓘ |
| inception | early 20th century ⓘ |
| influenced |
constructive approaches to mathematics
ⓘ
formalism in the philosophy of mathematics ⓘ model theory ⓘ ordinal analysis ⓘ proof theory ⓘ recursion theory ⓘ reverse mathematics ⓘ |
| influencedBy |
19th-century rigorization of analysis
ⓘ
David Hilbert’s axiomatic method ⓘ |
| legacy |
axiomatic treatment of mathematical theories
ⓘ
formal verification and automated theorem proving ⓘ modern proof theory ⓘ |
| mainProponent | David Hilbert ⓘ |
| namedAfter | David Hilbert ⓘ |
| notableWork |
Hilbert and Ackermann’s "Grundzüge der theoretischen Logik"
ⓘ
Hilbert problems ⓘ
surface form:
Hilbert’s 1900 Paris lecture
Hilbert’s 1920s lectures on proof theory ⓘ |
| opposedBy |
Luitzen Egbertus Jan Brouwer
ⓘ
surface form:
L. E. J. Brouwer
intuitionism ⓘ |
| relatedTo |
formalism
ⓘ
intuitionism ⓘ logicism ⓘ |
| status |
classically regarded as refuted in its original form
ⓘ
partially realized ⓘ |
| usesMethod |
finitistic methods
ⓘ
formal axiomatic systems ⓘ metamathematical reasoning ⓘ |
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: Hilbert’s program Description of subject: Hilbert’s program was an influential early-20th-century initiative in the foundations of mathematics that sought to formalize all of mathematics and prove its consistency using finitistic methods.
Referenced by (20)
Full triples — surface form annotated when it differs from this entity's canonical label.
this entity surface form:
Hilbert’s program in proof theory
this entity surface form:
Hilbert program
this entity surface form:
Hilbert's program
this entity surface form:
Hilbert's program
this entity surface form:
Hilbert program
this entity surface form:
Hilbert's program analysis
this entity surface form:
Hilbert–Bernays foundations of mathematics
this entity surface form:
Hilbert's program
this entity surface form:
Hilbert's program
subject surface form:
Grundzüge der theoretischen Logik
this entity surface form:
Hilbert program
this entity surface form:
Hilbert program
subject surface form:
Grundzüge der theoretischen Logik
this entity surface form:
Hilbert program in the foundations of mathematics
subject surface form:
Grundzüge der theoretischen Logik