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.
Aliases (3)
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
→
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’s 1900 Paris lecture → Hilbert’s 1920s lectures on proof theory → |
| opposedBy |
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 → |
Referenced by (6)
| Subject (surface form when different) | Predicate |
|---|---|
|
Jacques Herbrand
("Hilbert's program")
→
Wilhelm Ackermann ("Hilbert program") → |
contributedTo |
|
Entscheidungsproblem
→
|
historicalContext |
|
David Hilbert
("Hilbert’s program in proof theory")
→
|
notableIdea |
|
David Hilbert
→
|
notableWork |
|
Gödel's incompleteness theorems
("Hilbert's program")
→
|
relatedTo |