Grundgesetze der Arithmetik, Volume II

E105546

book logic work philosophy of mathematics work

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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All labels observed (4)

Label	Occurrences
Grundgesetze der Arithmetik	4
Grundgesetze der Arithmetik, Volume II canonical	2
Frege's Appendix to Grundgesetze der Arithmetik, Volume II	1
Grundgesetze der Arithmetik, Band II	1

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]

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
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, Band II ⓘ linked to: Grundgesetze der Arithmetik, Volume II
partOf	Grundgesetze der Arithmetik ⓘ linked to: Grundgesetze der Arithmetik, Volume II
philosophicalTradition	analytic philosophy ⓘ
relatedTo	Frege’s Basic Laws of Arithmetic ⓘ linked to: Frege’s system in "Grundgesetze der Arithmetik" Frege’s concept-script (Begriffsschrift) ⓘ linked to: Begriffsschrift Frege’s theory of extensions ⓘ
subject	Fregean logic ⓘ arithmetic ⓘ axiomatic systems ⓘ formal systems ⓘ logicism ⓘ
uses	Frege’s Basic Law V ⓘ linked to: Frege’s system in "Grundgesetze der Arithmetik" Frege’s formal notation ⓘ
volumeNumber	2 ⓘ

How these facts were elicited