Russell’s paradox

E2517

antimony in naive set theory logical paradox set-theoretic paradox

Russell’s paradox is a foundational logical contradiction in naive set theory that reveals problems with sets that contain themselves, leading to major developments in modern logic and the axiomatization of set theory.

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All labels observed (3)

Label	Occurrences
Russell paradox	7
Russell's paradox	7
Russell’s paradox canonical	6

How this entity was disambiguated

This entity first appeared as the object of triple T32515 — 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: Russell’s paradox
Context triple: [Bertrand Russell, knownFor, Russell’s paradox]

A. Bertrand Russell
Bertrand Russell was a British philosopher, logician, and social critic, renowned for his foundational work in analytic philosophy and contributions to logic, mathematics, and political thought.
B. Winston
Winston is the given name of Winston Churchill, the British statesman who led the United Kingdom during World War II and later served again as Prime Minister.
C. Moore
Moore is the middle name of Edward M. Kennedy, the long-serving U.S. senator from Massachusetts and prominent member of the Kennedy political family.
D. Trinity
The Trinity is the central Christian doctrine that God exists as one divine being in three distinct, co-equal persons: the Father, the Son, and the Holy Spirit.
E. Veritas
Veritas is the Latin word for "truth" and is famously used as the motto of Harvard University.
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: Russell’s paradox
Target entity description: Russell’s paradox is a foundational logical contradiction in naive set theory that reveals problems with sets that contain themselves, leading to major developments in modern logic and the axiomatization of set theory.

A. Bertrand Russell
Bertrand Russell was a British philosopher, logician, and social critic, renowned for his foundational work in analytic philosophy and contributions to logic, mathematics, and political thought.
B. Winston
Winston is the given name of Winston Churchill, the British statesman who led the United Kingdom during World War II and later served again as Prime Minister.
C. Moore
Moore is the middle name of Edward M. Kennedy, the long-serving U.S. senator from Massachusetts and prominent member of the Kennedy political family.
D. Trinity
The Trinity is the central Christian doctrine that God exists as one divine being in three distinct, co-equal persons: the Father, the Son, and the Holy Spirit.
E. Veritas
Veritas is the Latin word for "truth" and is famously used as the motto of Harvard University.
F. None of above. chosen

Statements (41)

Predicate	Object
instanceOf	antimony in naive set theory ⓘ logical paradox ⓘ set-theoretic paradox ⓘ
appearsIn	Principia Mathematica ⓘ surface form: "Principia Mathematica"
category	paradoxes in set theory ⓘ paradoxes of self-reference ⓘ
communicatedTo	Gottlob Frege ⓘ
concerns	naive set theory ⓘ self-membership of sets ⓘ the set of all sets that do not contain themselves ⓘ
discoveredBy	Bertrand Russell ⓘ
discoveryYear	1901 ⓘ
field	foundations of mathematics ⓘ mathematical logic ⓘ set theory ⓘ
formalizes	the contradiction arising from considering the set of all sets that are not members of themselves ⓘ
hasExampleFormulation	the set of all sets that are not members of themselves is a member of itself if and only if it is not a member of itself ⓘ
hasKeyQuestion	Does the set of all sets that are not members of themselves contain itself? ⓘ
impact	prompted rigorous foundations for mathematics ⓘ showed need to distinguish sets and proper classes ⓘ
influenced	Zermelo–Fraenkel set theory ⓘ the axiomatization of set theory ⓘ the development of modern logic ⓘ type theory ⓘ
ledTo	the development of Russell’s type theory ⓘ the introduction of restricted comprehension axioms ⓘ the separation axiom in Zermelo–Fraenkel set theory ⓘ
logicalForm	self-referential contradiction ⓘ
motivated	axiomatic set theory ⓘ
namedAfter	Bertrand Russell ⓘ
relatedTo	Barber paradox ⓘ Burali-Forti paradox ⓘ Cantor’s paradox ⓘ liar paradox ⓘ
resolutionApproach	restricting set formation by axioms ⓘ using type hierarchies to block self-membership ⓘ
shows	limitations of naive set theory ⓘ naive comprehension leads to contradiction ⓘ there is no set of all sets that are not members of themselves ⓘ unrestricted set formation is inconsistent ⓘ
undermined	Frege’s system in "Grundgesetze der Arithmetik" ⓘ

How these facts were elicited

Referenced by (20)

Full triples — surface form annotated when it differs from this entity's canonical label.

Bertrand Russell → knownFor → Russell’s paradox ⓘ

Barber paradox → illustrates → Russell’s paradox ⓘ

this entity surface form: Russell's paradox

Barber paradox → basedOn → Russell’s paradox ⓘ

this entity surface form: Russell's paradox

Barber paradox → relatedTo → Russell’s paradox ⓘ

this entity surface form: Russell's paradox

liar paradox → relatedTo → Russell’s paradox ⓘ

this entity surface form: Russell's paradox

Cantor’s paradox → relatedTo → Russell’s paradox ⓘ

Zermelo–Fraenkel set theory → designedToAvoid → Russell’s paradox ⓘ