Principles of Mathematical Logic
E838589
Principles of Mathematical Logic is a foundational work in mathematical logic by David Hilbert and Wilhelm Ackermann that systematically develops the formal underpinnings of logical reasoning and proof theory.
All labels observed (2)
| Label | Occurrences |
|---|---|
| Principles of Mathematical Logic canonical | 2 |
| Principles of Mathematical Logic (English edition) | 1 |
How this entity was disambiguated
This entity first appeared as the object of triple T10055634 — 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: Principles of Mathematical Logic Context triple: [Grundzüge der theoretischen Logik, translatedAs, Principles of Mathematical Logic]
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A.
Introduction to Metamathematics
Introduction to Metamathematics is a classic 1952 textbook by Stephen Kleene that systematically develops the foundations of mathematical logic and recursion theory.
-
B.
New Foundations for Mathematical Logic
New Foundations for Mathematical Logic is W.V.O. Quine’s influential essay proposing an alternative set theory, known as "New Foundations," aimed at resolving paradoxes while preserving a broad, intuitive universe of sets.
-
C.
Grundgesetze der Arithmetik, Volume I
Grundgesetze der Arithmetik, Volume I is Gottlob Frege’s foundational work in logic and the philosophy of mathematics, in which he develops his formal system aimed at deriving arithmetic from purely logical principles.
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D.
Arithmetices principia, nova methodo exposita
Arithmetices principia, nova methodo exposita is Giuseppe Peano’s foundational work in mathematical logic that presents an axiomatization of arithmetic using symbolic notation.
-
E.
From Frege to Gödel: A Source Book in Mathematical Logic, 1879–1931
From Frege to Gödel: A Source Book in Mathematical Logic, 1879–1931 is a landmark anthology that collects and translates many of the foundational papers in modern mathematical logic from the late 19th to early 20th century.
- 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: Principles of Mathematical Logic Target entity description: Principles of Mathematical Logic is a foundational work in mathematical logic by David Hilbert and Wilhelm Ackermann that systematically develops the formal underpinnings of logical reasoning and proof theory.
-
A.
Introduction to Metamathematics
Introduction to Metamathematics is a classic 1952 textbook by Stephen Kleene that systematically develops the foundations of mathematical logic and recursion theory.
-
B.
New Foundations for Mathematical Logic
New Foundations for Mathematical Logic is W.V.O. Quine’s influential essay proposing an alternative set theory, known as "New Foundations," aimed at resolving paradoxes while preserving a broad, intuitive universe of sets.
-
C.
Grundgesetze der Arithmetik, Volume I
Grundgesetze der Arithmetik, Volume I is Gottlob Frege’s foundational work in logic and the philosophy of mathematics, in which he develops his formal system aimed at deriving arithmetic from purely logical principles.
-
D.
Arithmetices principia, nova methodo exposita
Arithmetices principia, nova methodo exposita is Giuseppe Peano’s foundational work in mathematical logic that presents an axiomatization of arithmetic using symbolic notation.
-
E.
From Frege to Gödel: A Source Book in Mathematical Logic, 1879–1931
From Frege to Gödel: A Source Book in Mathematical Logic, 1879–1931 is a landmark anthology that collects and translates many of the foundational papers in modern mathematical logic from the late 19th to early 20th century.
- F. None of above. chosen
Statements (47)
| Predicate | Object |
|---|---|
| instanceOf |
book
ⓘ
work in mathematical logic ⓘ |
| aim |
to formalize logical reasoning
ⓘ
to provide a systematic development of mathematical logic ⓘ to support the foundations of mathematics ⓘ |
| author |
David Hilbert
ⓘ
Wilhelm Ackermann ⓘ |
| contribution |
clarification of the notion of formal theory
ⓘ
development of formal proof systems ⓘ early systematic exposition of first-order logic ⓘ |
| countryOfOrigin | Germany ⓘ |
| field |
foundations of mathematics
ⓘ
mathematical logic ⓘ proof theory ⓘ |
| genre |
mathematics textbook
ⓘ
non-fiction ⓘ |
| hasEdition | second edition ⓘ |
| hasEnglishTranslation |
Principles of Mathematical Logic (English edition)
ⓘ
linked to:
Principles of Mathematical Logic
|
| hasSubject |
formal deduction
ⓘ
logical calculi ⓘ logical consequence ⓘ predicate calculus ⓘ sentential calculus ⓘ |
| historicalPeriod | 20th century ⓘ |
| influenced |
Gerhard Gentzen
ⓘ
Hilbert program ⓘ
linked to:
Hilbert’s program
Kurt Gödel ⓘ modern proof theory ⓘ |
| influencedBy |
Alfred North Whitehead
ⓘ
Bertrand Russell ⓘ Gottlob Frege ⓘ |
| language | German ⓘ |
| notableFor |
foundational role in mathematical logic
ⓘ
influence on later work in proof theory ⓘ |
| originalTitle |
Grundzüge der theoretischen Logik
ⓘ
linked to:
"Grundzüge der theoretischen Logik"
|
| partOf |
Hilbert program
ⓘ
linked to:
Hilbert’s program
|
| publicationYear | 1928 ⓘ |
| publisher | Springer ⓘ |
| topic |
axiomatic systems
ⓘ
completeness ⓘ consistency ⓘ decision problems ⓘ first-order logic ⓘ formalization of logic ⓘ propositional logic ⓘ |
| uses |
formal languages
ⓘ
symbolic notation ⓘ |
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: Principles of Mathematical Logic Description of subject: Principles of Mathematical Logic is a foundational work in mathematical logic by David Hilbert and Wilhelm Ackermann that systematically develops the formal underpinnings of logical reasoning and proof theory.
Referenced by (3)
Full triples — surface form annotated when it differs from this entity's canonical label.
subject linked to:
Hilbert and Ackermann’s "Grundzüge der theoretischen Logik"
subject linked to:
Hilbert and Ackermann’s "Grundzüge der theoretischen Logik"
Principles of Mathematical Logic
→
hasEnglishTranslation
→
Principles of Mathematical Logic (English edition)
ⓘ
linked to: Principles of Mathematical Logic