Grundgesetze der Arithmetik, Volume II
E105546
Grundgesetze der Arithmetik, Volume II is the second volume of Gottlob Frege’s foundational work in logic and the philosophy of mathematics, in which he further develops and applies his formal system for arithmetic.
All labels observed (4)
How this entity was disambiguated
This entity first appeared as the object of triple T857951 — 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: Grundgesetze der Arithmetik, Volume II Context triple: [Frege’s system in "Grundgesetze der Arithmetik", foundInVolume, Grundgesetze der Arithmetik, Volume II]
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A.
Die Grundlagen der Arithmetik
Die Grundlagen der Arithmetik is Gottlob Frege’s seminal philosophical work that lays the logical foundations of arithmetic and advances the logicist thesis that arithmetic is reducible to pure logic.
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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.
-
C.
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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D.
Lectures on the Logic of Arithmetic
Lectures on the Logic of Arithmetic is an educational work by Mary Everest Boole that explores the foundations and teaching of arithmetic through logical and psychological principles.
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E.
Begriffsschrift
Begriffsschrift is Gottlob Frege’s groundbreaking 1879 work that introduced a formal logical notation and is widely regarded as the foundation of modern symbolic logic.
- 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: Grundgesetze der Arithmetik, Volume II Target entity description: Grundgesetze der Arithmetik, Volume II is the second volume of Gottlob Frege’s foundational work in logic and the philosophy of mathematics, in which he further develops and applies his formal system for arithmetic.
-
A.
Die Grundlagen der Arithmetik
Die Grundlagen der Arithmetik is Gottlob Frege’s seminal philosophical work that lays the logical foundations of arithmetic and advances the logicist thesis that arithmetic is reducible to pure logic.
-
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.
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.
-
D.
Lectures on the Logic of Arithmetic
Lectures on the Logic of Arithmetic is an educational work by Mary Everest Boole that explores the foundations and teaching of arithmetic through logical and psychological principles.
-
E.
Begriffsschrift
Begriffsschrift is Gottlob Frege’s groundbreaking 1879 work that introduced a formal logical notation and is widely regarded as the foundation of modern symbolic logic.
- F. None of above. chosen
Statements (41)
| Predicate | Object |
|---|---|
| instanceOf |
book
ⓘ
logic work ⓘ philosophy of mathematics work ⓘ |
| applies | the formal system introduced in Volume I ⓘ |
| author | Gottlob Frege ⓘ |
| countryOfOrigin | Germany ⓘ |
| field |
foundations of mathematics
ⓘ
logic ⓘ philosophy of mathematics ⓘ |
| follows | Grundgesetze der Arithmetik, Volume I ⓘ |
| genre |
mathematical logic
ⓘ
non-fiction ⓘ |
| hasAuthorialIntention | to provide a logical foundation for arithmetic ⓘ |
| hasCentralTheme |
formal derivation of arithmetic laws
ⓘ
logical analysis of number ⓘ reduction of arithmetic to logic ⓘ |
| hasImpactOn |
debates about the consistency of Frege’s system
ⓘ
subsequent work on logical paradoxes ⓘ |
| hasWorkExample | derivations of arithmetic theorems from logical axioms ⓘ |
| historicalContext | late 19th-century foundational crisis in mathematics ⓘ |
| influenced |
20th-century analytic philosophy
ⓘ
philosophy of mathematics ⓘ set theory discussions ⓘ |
| influencedBy | Gottlob Frege’s earlier logical writings ⓘ |
| language | German ⓘ |
| notableFor |
development and application of Frege’s logical system to arithmetic
ⓘ
role in the history of logicism ⓘ |
| originalTitle |
Grundgesetze der Arithmetik, Volume II
self-linksurface differs
ⓘ
surface form:
Grundgesetze der Arithmetik, Band II
|
| partOf |
Grundgesetze der Arithmetik, Volume II
self-linksurface differs
ⓘ
surface form:
Grundgesetze der Arithmetik
|
| philosophicalTradition | analytic philosophy ⓘ |
| relatedTo |
Frege’s system in "Grundgesetze der Arithmetik"
ⓘ
surface form:
Frege’s Basic Laws of Arithmetic
Begriffsschrift ⓘ
surface form:
Frege’s concept-script (Begriffsschrift)
Frege’s theory of extensions ⓘ |
| subject |
Fregean logic
ⓘ
arithmetic ⓘ axiomatic systems ⓘ formal systems ⓘ logicism ⓘ |
| uses |
Frege’s system in "Grundgesetze der Arithmetik"
ⓘ
surface form:
Frege’s Basic Law V
Frege’s formal notation ⓘ |
| volumeNumber | 2 ⓘ |
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: Grundgesetze der Arithmetik, Volume II Description of subject: Grundgesetze der Arithmetik, Volume II is the second volume of Gottlob Frege’s foundational work in logic and the philosophy of mathematics, in which he further develops and applies his formal system for arithmetic.
Referenced by (7)
Full triples — surface form annotated when it differs from this entity's canonical label.
Frege’s system in "Grundgesetze der Arithmetik"
→
foundInVolume
→
Grundgesetze der Arithmetik, Volume II
ⓘ
this entity surface form:
Grundgesetze der Arithmetik
subject surface form:
Friedrich Ludwig Gottlob Frege
this entity surface form:
Grundgesetze der Arithmetik
this entity surface form:
Grundgesetze der Arithmetik
this entity surface form:
Frege's Appendix to Grundgesetze der Arithmetik, Volume II
Grundgesetze der Arithmetik, Volume II
→
partOf
→
Grundgesetze der Arithmetik, Volume II
self-linksurface differs
ⓘ
this entity surface form:
Grundgesetze der Arithmetik
Grundgesetze der Arithmetik, Volume II
→
originalTitle
→
Grundgesetze der Arithmetik, Volume II
self-linksurface differs
ⓘ
this entity surface form:
Grundgesetze der Arithmetik, Band II