Grundgesetze der Arithmetik, Volume I
E471153
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.
All labels observed (3)
| Label | Occurrences |
|---|---|
| Grundgesetze der Arithmetik | 3 |
| Grundgesetze der Arithmetik, Volume I canonical | 2 |
| Grundgesetze der Arithmetik, Band I | 1 |
How this entity was disambiguated
This entity first appeared as the object of triple T4754154 — 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 I Context triple: [Grundgesetze der Arithmetik, Volume II, follows, Grundgesetze der Arithmetik, Volume I]
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A.
Grundgesetze der Arithmetik, Volume II
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.
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B.
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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C.
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.
-
D.
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.
-
E.
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.
- 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 I Target entity description: 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.
-
A.
Grundgesetze der Arithmetik, Volume II
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.
-
B.
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.
-
C.
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.
-
D.
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.
-
E.
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.
- F. None of above. chosen
Statements (45)
| Predicate | Object |
|---|---|
| instanceOf |
book
ⓘ
philosophical work ⓘ work on logic ⓘ |
| aim | to derive arithmetic from purely logical principles ⓘ |
| author | Gottlob Frege ⓘ |
| centuryOfPublication | 19th century ⓘ |
| concerns |
concept of number
ⓘ
extensions of concepts ⓘ foundations of arithmetic ⓘ |
| countryOfOrigin | Germany ⓘ |
| develops | formal logical system ⓘ |
| field |
foundations of mathematics
ⓘ
logic ⓘ philosophy of mathematics ⓘ |
| genre | academic monograph ⓘ |
| hasImpactOn | set-theoretic paradoxes discussion ⓘ |
| hasKeyConcept |
course-of-values operator
ⓘ
definition of natural numbers ⓘ identity of value-ranges ⓘ logical derivation of arithmetic laws ⓘ |
| hasVolumeNumber | 1 ⓘ |
| influenced |
Bertrand Russell
ⓘ
analytic philosophy ⓘ logicism of Russell and Whitehead ⓘ mathematical logic ⓘ philosophy of language ⓘ |
| introduces | Basic Law V ⓘ |
| logicalSystem | Frege’s Begriffsschrift-based notation ⓘ |
| mainTopic |
arithmetic
ⓘ
axiomatic method ⓘ formal systems ⓘ logicism ⓘ philosophical logic ⓘ |
| method | axiomatic deduction ⓘ |
| originalLanguage | German ⓘ |
| originalTitle |
Grundgesetze der Arithmetik, Band I
ⓘ
linked to:
Grundgesetze der Arithmetik, Volume I
|
| partOf |
Grundgesetze der Arithmetik
ⓘ
linked to:
Grundgesetze der Arithmetik, Volume I
|
| placeOfPublication | Jena ⓘ |
| precedes | Grundgesetze der Arithmetik, Volume II ⓘ |
| publicationYear | 1893 ⓘ |
| publisher | Hermann Pohle ⓘ |
| relatedTo |
Die Grundlagen der Arithmetik
ⓘ
Frege’s earlier work Begriffsschrift ⓘ
linked to:
Begriffsschrift
|
| title | Grundgesetze der Arithmetik, Volume I ⓘ |
| uses | second-order logic ⓘ |
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 I Description of subject: 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.
Referenced by (6)
Full triples — surface form annotated when it differs from this entity's canonical label.
linked to: Grundgesetze der Arithmetik, Volume I
subject linked to:
Gottlob
linked to: Grundgesetze der Arithmetik, Volume I
linked to: Grundgesetze der Arithmetik, Volume I
linked to: Grundgesetze der Arithmetik, Volume I