Die Grundlagen der Arithmetik
E51851
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.
All labels observed (4)
| Label | Occurrences |
|---|---|
| Die Grundlagen der Arithmetik canonical | 6 |
| Frege’s Grundlagen der Arithmetik | 1 |
| The Foundations of Arithmetic | 1 |
| The principles of arithmetic, presented by a new method | 1 |
How this entity was disambiguated
This entity first appeared as the object of triple T403548 — 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: Die Grundlagen der Arithmetik Context triple: [Gottlob Frege, notableWork, Die Grundlagen der Arithmetik]
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A.
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.
-
B.
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.
-
C.
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.
-
D.
Disquisitiones Arithmeticae
Disquisitiones Arithmeticae is a foundational 1801 treatise on number theory that systematically developed the subject and introduced many of its central concepts and methods.
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E.
Elementary Mathematics from an Advanced Standpoint
"Elementary Mathematics from an Advanced Standpoint" is a classic three-volume work by Felix Klein that reexamines school-level mathematics through the lens of modern, rigorous mathematical theory and pedagogy.
- 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: Die Grundlagen der Arithmetik Target entity description: 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.
-
A.
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.
-
B.
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.
-
C.
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.
-
D.
Disquisitiones Arithmeticae
Disquisitiones Arithmeticae is a foundational 1801 treatise on number theory that systematically developed the subject and introduced many of its central concepts and methods.
-
E.
Elementary Mathematics from an Advanced Standpoint
"Elementary Mathematics from an Advanced Standpoint" is a classic three-volume work by Felix Klein that reexamines school-level mathematics through the lens of modern, rigorous mathematical theory and pedagogy.
- F. None of above. chosen
Statements (47)
| Predicate | Object |
|---|---|
| instanceOf |
book
ⓘ
philosophical work ⓘ |
| aim |
to analyze the meaning of numerical statements
ⓘ
to provide a purely logical foundation for arithmetic ⓘ |
| author | Gottlob Frege ⓘ |
| centralConcept |
cardinal number
ⓘ
concept of zero ⓘ definition by abstraction ⓘ extension of a concept ⓘ identity ⓘ |
| countryOfOrigin | Germany ⓘ |
| field |
foundations of mathematics
ⓘ
mathematical logic ⓘ |
| firstPublishedIn | Breslau ⓘ |
| genre |
analytic philosophy
ⓘ
logic ⓘ philosophy of mathematics literature ⓘ |
| hasEnglishTitle |
Die Grundlagen der Arithmetik
self-linksurface differs
ⓘ
surface form:
The Foundations of Arithmetic
|
| hasPart |
analysis of the concept of number
ⓘ
critique of psychologism in arithmetic ⓘ derivation of basic laws of number from logic ⓘ discussion of identity and equality ⓘ |
| historicalSignificance |
major early work in modern logicism
ⓘ
one of the founding texts of analytic philosophy of mathematics ⓘ |
| influenced |
Bertrand Russell
ⓘ
Ludwig Wittgenstein ⓘ Rudolf Carnap ⓘ analytic philosophy ⓘ modern logic ⓘ philosophy of language ⓘ |
| influencedBy |
Immanuel Kant
ⓘ
Leibnizian logic ⓘ |
| language | German ⓘ |
| mainThesis |
arithmetic is reducible to pure logic
ⓘ
numbers are logical objects ⓘ |
| notableIdea |
context principle about meaning in sentences
ⓘ
numbers as extensions of concepts ⓘ |
| originalTitle | Die Grundlagen der Arithmetik self-link ⓘ |
| philosophicalStance | logicism ⓘ |
| positionOnPsychologism | rejects psychologism about arithmetic ⓘ |
| publicationYear | 1884 ⓘ |
| publisher | Verlag Wilhelm Koebner ⓘ |
| subject |
arithmetic
ⓘ
logic ⓘ logicism ⓘ number theory ⓘ philosophy of mathematics ⓘ |
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: Die Grundlagen der Arithmetik Description of subject: 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.
Referenced by (9)
Full triples — surface form annotated when it differs from this entity's canonical label.
Die Grundlagen der Arithmetik
→
hasEnglishTitle
→
Die Grundlagen der Arithmetik
self-linksurface differs
ⓘ
this entity surface form:
The Foundations of Arithmetic
subject surface form:
Friedrich Ludwig Gottlob Frege
this entity surface form:
Frege’s Grundlagen der Arithmetik
subject surface form:
Gottlob Frege
this entity surface form:
The principles of arithmetic, presented by a new method