Frege’s system in "Grundgesetze der Arithmetik"
E18534
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.
All labels observed (11)
How this entity was disambiguated
This entity first appeared as the object of triple T124582 — 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: Frege’s system in "Grundgesetze der Arithmetik" Context triple: [Russell’s paradox, undermined, Frege’s system in "Grundgesetze der Arithmetik"]
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A.
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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B.
The Mathematical Analysis of Logic
The Mathematical Analysis of Logic is George Boole’s pioneering 1847 work that laid the foundations of symbolic logic and helped initiate the algebraic treatment of logical reasoning.
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C.
An Investigation of the Laws of Thought
An Investigation of the Laws of Thought is George Boole’s foundational 1854 treatise that established Boolean algebra and helped lay the groundwork for modern mathematical logic and computer science.
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D.
The Scientific Conception of the World: The Vienna Circle
"The Scientific Conception of the World: The Vienna Circle" is a foundational manifesto that articulates the Vienna Circle’s program of scientifically oriented philosophy, emphasizing empirical verification, logical analysis, and the rejection of metaphysics.
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E.
Tractatus Logico-Philosophicus
Tractatus Logico-Philosophicus is Ludwig Wittgenstein’s early 20th-century philosophical work that attempts to define the relationship between language, thought, and reality through a highly structured, logical framework.
- 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: Frege’s system in "Grundgesetze der Arithmetik" Target entity description: 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.
-
A.
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.
-
B.
The Mathematical Analysis of Logic
The Mathematical Analysis of Logic is George Boole’s pioneering 1847 work that laid the foundations of symbolic logic and helped initiate the algebraic treatment of logical reasoning.
-
C.
An Investigation of the Laws of Thought
An Investigation of the Laws of Thought is George Boole’s foundational 1854 treatise that established Boolean algebra and helped lay the groundwork for modern mathematical logic and computer science.
-
D.
The Scientific Conception of the World: The Vienna Circle
"The Scientific Conception of the World: The Vienna Circle" is a foundational manifesto that articulates the Vienna Circle’s program of scientifically oriented philosophy, emphasizing empirical verification, logical analysis, and the rejection of metaphysics.
-
E.
Tractatus Logico-Philosophicus
Tractatus Logico-Philosophicus is Ludwig Wittgenstein’s early 20th-century philosophical work that attempts to define the relationship between language, thought, and reality through a highly structured, logical framework.
- F. None of above. chosen
Statements (49)
| Predicate | Object |
|---|---|
| instanceOf |
formal logical system
ⓘ
foundational system for arithmetic ⓘ second-order logical system ⓘ |
| aimsTo | provide a logical foundation for arithmetic ⓘ |
| basedOn | second-order logic ⓘ |
| centralAxiom | Basic Law V ⓘ |
| creator | Gottlob Frege ⓘ |
| describedInWork |
Frege’s system in "Grundgesetze der Arithmetik"
self-linksurface differs
ⓘ
surface form:
Grundgesetze der Arithmetik
|
| formalizes | Hume’s Principle (derivable, not postulated) ⓘ |
| formalLanguage | ideography (Begriffsschrift) ⓘ |
| foundInVolume |
Frege’s system in "Grundgesetze der Arithmetik"
self-linksurface differs
ⓘ
surface form:
Grundgesetze der Arithmetik, Volume I
Grundgesetze der Arithmetik, Volume II ⓘ |
| goal | derive Peano axioms for arithmetic from purely logical principles ⓘ |
| hasComponent |
axioms for identity
ⓘ
axioms for quantification ⓘ axioms for truth-functions ⓘ definition of finite cardinal numbers ⓘ definition of numbers as extensions ⓘ definition of successor ⓘ proofs of basic laws of arithmetic ⓘ |
| historicalImpact |
influenced development of axiomatic set theory
ⓘ
influenced development of type theory ⓘ influenced later work in model theory and proof theory ⓘ triggered crisis in foundations of mathematics ⓘ |
| includesAxiom | Basic Law V ⓘ |
| inconsistencyRevealedBy | Russell’s paradox ⓘ |
| inconsistencySource | Basic Law V ⓘ |
| influenced |
Alfred North Whitehead
ⓘ
Bertrand Russell ⓘ Principia Mathematica ⓘ Zermelo–Fraenkel set theory ⓘ
surface form:
Zermelo–Fraenkel set theory (indirectly)
neo-logicist programs in the philosophy of mathematics ⓘ |
| intendedToShow | that arithmetic is reducible to logic ⓘ |
| isInconsistent | true ⓘ |
| logicalFramework | axiomatic calculus for functions and objects ⓘ |
| logicalNotion | course-of-values operator (extension operator) ⓘ |
| paradoxType | set-theoretic paradox of the extension of the concept "not self-membered" ⓘ |
| philosophicalProgram | logicism ⓘ |
| quantificationType | second-order quantification over concepts ⓘ |
| responseByFrege | attempted modification of Basic Law V in Appendix to Volume II ⓘ |
| treats | numbers as extensions of concepts ⓘ |
| treatsAsObjects | extensions of concepts ⓘ |
| uses |
extensionality for concepts
ⓘ
function–argument analysis of propositions ⓘ truth-values as objects ⓘ |
| usesDistinction |
between objects and concepts
ⓘ
between sense and reference (in the surrounding theory) ⓘ |
| yearFirstVolumePublished | 1893 ⓘ |
| yearSecondVolumePublished | 1903 ⓘ |
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: Frege’s system in "Grundgesetze der Arithmetik" Description of subject: 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.
Referenced by (14)
Full triples — surface form annotated when it differs from this entity's canonical label.
this entity surface form:
Grundgesetze der Arithmetik
Frege’s system in "Grundgesetze der Arithmetik"
→
describedInWork
→
Frege’s system in "Grundgesetze der Arithmetik"
self-linksurface differs
ⓘ
this entity surface form:
Grundgesetze der Arithmetik
Frege’s system in "Grundgesetze der Arithmetik"
→
foundInVolume
→
Frege’s system in "Grundgesetze der Arithmetik"
self-linksurface differs
ⓘ
this entity surface form:
Grundgesetze der Arithmetik, Volume I
this entity surface form:
Fregean quantifier notation
this entity surface form:
Fregean function–argument analysis
this entity surface form:
Grundgesetze der Arithmetik, Volume I
this entity surface form:
Frege's logicist program
Hume’s Principle (derivable, not postulated)
→
holdsIn
→
Frege’s system in "Grundgesetze der Arithmetik"
ⓘ
this entity surface form:
Frege’s logical system
Hume’s Principle (derivable, not postulated)
→
isDerivedIn
→
Frege’s system in "Grundgesetze der Arithmetik"
ⓘ
this entity surface form:
Frege’s logical system
this entity surface form:
Frege’s Basic Law V
Grundgesetze der Arithmetik, Volume II
→
relatedTo
→
Frege’s system in "Grundgesetze der Arithmetik"
ⓘ
this entity surface form:
Frege’s Basic Laws of Arithmetic
this entity surface form:
Frege's system in Grundgesetze der Arithmetik
this entity surface form:
Frege's Basic Law V