Russell’s paradox
E2517
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.
All labels observed (3)
| Label | Occurrences |
|---|---|
| Russell's paradox | 8 |
| Russell paradox | 7 |
| Russell’s paradox canonical | 7 |
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]
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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.
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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.
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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.
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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.
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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"
ⓘ
linked to:
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
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: Russell’s paradox Description of subject: 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.
Referenced by (22)
Full triples — surface form annotated when it differs from this entity's canonical label.
linked to: Russell’s paradox
linked to: Russell’s paradox
linked to: Russell’s paradox
linked to: Russell’s paradox
linked to: Russell’s paradox
linked to: Russell’s paradox
linked to: Russell’s paradox
linked to: Russell’s paradox
linked to: Russell’s paradox
linked to: Russell’s paradox
linked to: Russell’s paradox
linked to: Russell’s paradox
linked to: Russell’s paradox
linked to: Russell’s paradox
linked to: Russell’s paradox