Basic Law V
E101761
Basic Law V is a central axiom in Frege’s logical system that equates the extensions of concepts with identical truth conditions, and whose inconsistency famously undermined his logicist foundation for arithmetic.
All labels observed (1)
| Label | Occurrences |
|---|---|
| Basic Law V canonical | 4 |
How this entity was disambiguated
This entity first appeared as the object of triple T857936 — 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: Basic Law V Context triple: [Frege’s system in "Grundgesetze der Arithmetik", includesAxiom, Basic Law V]
-
A.
Basic Law of the Hong Kong Special Administrative Region
The Basic Law of the Hong Kong Special Administrative Region is Hong Kong's mini-constitution, outlining its system of governance, rights, and autonomy under the "one country, two systems" framework within the People's Republic of China.
-
B.
Basic Law for the Federal Republic of Germany
The Basic Law for the Federal Republic of Germany is the country’s foundational legal charter, establishing its democratic, federal, and constitutional order after World War II.
-
C.
Constitution of the People's Republic of China
The Constitution of the People's Republic of China is the country's fundamental law that defines the structure of the state, the leadership role of the Communist Party, and the rights and duties of citizens.
-
D.
Constitution of 1976
The Constitution of 1976 is Portugal’s post-revolution democratic charter that redefined the country’s political system, civil liberties, and institutional framework after the Carnation Revolution.
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E.
Basic Law
Basic Law is the constitutional charter of the Federal Republic of Germany, establishing its fundamental political and legal order.
- 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: Basic Law V Target entity description: Basic Law V is a central axiom in Frege’s logical system that equates the extensions of concepts with identical truth conditions, and whose inconsistency famously undermined his logicist foundation for arithmetic.
-
A.
Basic Law of the Hong Kong Special Administrative Region
The Basic Law of the Hong Kong Special Administrative Region is Hong Kong's mini-constitution, outlining its system of governance, rights, and autonomy under the "one country, two systems" framework within the People's Republic of China.
-
B.
Basic Law for the Federal Republic of Germany
The Basic Law for the Federal Republic of Germany is the country’s foundational legal charter, establishing its democratic, federal, and constitutional order after World War II.
-
C.
Constitution of the People's Republic of China
The Constitution of the People's Republic of China is the country's fundamental law that defines the structure of the state, the leadership role of the Communist Party, and the rights and duties of citizens.
-
D.
Constitution of 1976
The Constitution of 1976 is Portugal’s post-revolution democratic charter that redefined the country’s political system, civil liberties, and institutional framework after the Carnation Revolution.
-
E.
Basic Law
Basic Law is the constitutional charter of the Federal Republic of Germany, establishing its fundamental political and legal order.
- F. None of above. chosen
Statements (48)
| Predicate | Object |
|---|---|
| instanceOf |
axiom schema
ⓘ
logical axiom ⓘ principle in the philosophy of mathematics ⓘ |
| aimedToJustify | definition of numbers as extensions of concepts ⓘ |
| alsoWrittenAs | ∀F∀G(εF = εG ↔ ∀x(Fx ↔ Gx)) ⓘ |
| appliesTo |
first-level concepts
ⓘ
second-level concepts ⓘ |
| author | Gottlob Frege ⓘ |
| category | abstraction principle for concepts ⓘ |
| centralIn | Frege's logicist program ⓘ |
| concerns | extensions of concepts ⓘ |
| criticizedBy |
Bertrand Russell
ⓘ
later neo-logicists ⓘ |
| discussedIn |
Frege's Appendix to Grundgesetze der Arithmetik, Volume II
ⓘ
linked to:
Grundgesetze der Arithmetik, Volume II
|
| equates |
extensions of coextensive concepts
ⓘ
extensions of concepts with identical truth conditions ⓘ |
| expresses | that concepts with the same extension have the same course-of-values ⓘ |
| formalizes | principle of extensionality for concepts ⓘ |
| historicalImpact |
influenced axiomatic set theory
ⓘ
motivated development of type theory ⓘ triggered revisions of logic and set theory ⓘ |
| inconsistencyDiscoveredIn | 1902 ⓘ |
| involves |
biconditional relating extension identity and coextensiveness
ⓘ
identity of extensions ⓘ |
| isInconsistentWith |
naive set-theoretic reasoning
ⓘ
unrestricted comprehension for concepts ⓘ |
| leadsTo |
Russell's paradox
ⓘ
linked to:
Russell’s paradox
|
| logicalForm | abstraction principle ⓘ |
| partOf |
Frege's logical system
ⓘ
Grundgesetze der Arithmetik ⓘ
linked to:
Grundgesetze der Arithmetik, Volume II
|
| publicationYear | 1893 ⓘ |
| relatedTo |
Axiom of Extensionality in set theory
ⓘ
naive comprehension schema ⓘ |
| requires | second-order quantification over concepts ⓘ |
| roleIn | derivation of arithmetic from logic ⓘ |
| statedIn | Grundgesetze der Arithmetik, Volume I ⓘ |
| statusInModernLogic | known to be inconsistent with second-order logic plus full comprehension ⓘ |
| studiedIn |
foundations of arithmetic
ⓘ
history of logic ⓘ philosophy of mathematics ⓘ |
| symbolicallyFormulatedAs | ∀F∀G(Ext(F) = Ext(G) ↔ ∀x(Fx ↔ Gx)) ⓘ |
| undermined | Frege's original logicist foundation for arithmetic ⓘ |
| usesNotion |
course-of-values
ⓘ
extension of a concept ⓘ |
| wasShownInconsistentBy | Bertrand Russell ⓘ |
| weakenedVariantsInclude |
Hume's Principle
ⓘ
linked to:
Hume’s Principle (derivable, not postulated)
predicative restrictions on abstraction principles ⓘ |
| weakenedVariantsUsedIn | neo-logicism ⓘ |
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: Basic Law V Description of subject: Basic Law V is a central axiom in Frege’s logical system that equates the extensions of concepts with identical truth conditions, and whose inconsistency famously undermined his logicist foundation for arithmetic.
Referenced by (4)
Full triples — surface form annotated when it differs from this entity's canonical label.