Triple

T124578
Position Surface form Disambiguated ID Type / Status
Subject Russell’s paradox E2517 entity
Predicate relatedTo P37 FINISHED
Object Cantor’s paradox
Cantor’s paradox is a foundational result in set theory showing that the “set of all sets” cannot exist because its power set would have a strictly larger cardinality, leading to a contradiction.
E14593 NE FINISHED

How this triple was built (4 steps)

Every LLM step that produced this triple, in pipeline order — named-entity classification, the disambiguation choices (the exact options shown, with the pick highlighted), and the generated description. The batch + timestamp of each is in the Provenance table below.

NER Named-entity recognition gpt-5-mini
Instruction
Given a phrase, classify it is english named entity (e.g., persons, organizations, works of art) in Latin script, or not (e.g., literals, dates, URLs, verbose phrases). For disambiguation, the statement where the phrase occurs as object is also given. Please return a JSON object with `phrase` (string, the phrase being analyzed) and `is_ne` (boolean, indicating whether the phrase is a Named Entity).
Input
Phrase: Cantor’s paradox | Statement: [Russell’s paradox, relatedTo, Cantor’s paradox]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07
Target entity: Cantor’s paradox
Context triple: [Russell’s paradox, relatedTo, Cantor’s paradox]
  • A. Burali-Forti paradox
    The Burali-Forti paradox is a foundational logical contradiction in set theory that arises from considering the set of all ordinal numbers, showing that such a totality cannot consistently exist as a set.
  • B. Russell’s 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.
  • C. Barber paradox
    The Barber paradox is a self-referential logical puzzle about a barber who shaves all and only those who do not shave themselves, illustrating a contradiction similar to Russell’s paradox.
  • D. Zermelo–Fraenkel set theory
    Zermelo–Fraenkel set theory is the standard axiomatic framework for modern set theory, designed to avoid paradoxes and provide a rigorous foundation for much of mathematics.
  • E. On Contradiction
    "On Contradiction" is a 1937 philosophical essay by Mao Zedong that systematically applies and develops Marxist dialectical materialism to analyze the nature and role of contradictions in social and historical processes.
  • F. None of above. chosen
  • G. Unsure - the case is ambiguous/there is not enough information to decide.
NEDg Description generation gpt-5.1
Instruction
Generate a one-sentence description of the target entity. 
You are given a context triple in the form (subject, predicate, object), where the object is the target entity. 
# Instructions
Use the triple to infer relevant information about the entity. Describe the entity based on what is most defining, well-known. 
Avoid repeating the information from the triple, unless really essential.
# Response Format
Return only the sentence: "Description: [one-sentence description of the target entity]"
Input
Entity: Cantor’s paradox
Triple: [Russell’s paradox, relatedTo, Cantor’s paradox]
Generated description
Cantor’s paradox is a foundational result in set theory showing that the “set of all sets” cannot exist because its power set would have a strictly larger cardinality, leading to a contradiction.
NED2 Entity disambiguation (via description) gpt-5-mini-2025-08-07
Target entity: Cantor’s paradox
Target entity description: Cantor’s paradox is a foundational result in set theory showing that the “set of all sets” cannot exist because its power set would have a strictly larger cardinality, leading to a contradiction.
  • A. Burali-Forti paradox
    The Burali-Forti paradox is a foundational logical contradiction in set theory that arises from considering the set of all ordinal numbers, showing that such a totality cannot consistently exist as a set.
  • B. Russell’s 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.
  • C. Barber paradox
    The Barber paradox is a self-referential logical puzzle about a barber who shaves all and only those who do not shave themselves, illustrating a contradiction similar to Russell’s paradox.
  • D. Zermelo–Fraenkel set theory
    Zermelo–Fraenkel set theory is the standard axiomatic framework for modern set theory, designed to avoid paradoxes and provide a rigorous foundation for much of mathematics.
  • E. On Contradiction
    "On Contradiction" is a 1937 philosophical essay by Mao Zedong that systematically applies and develops Marxist dialectical materialism to analyze the nature and role of contradictions in social and historical processes.
  • F. None of above. chosen

Provenance (5 batches)

The batch behind each pipeline step, in order, with when it ran. Timestamps are batch-level — stages were processed in waves, so the object chain (NER → NED1 → NEDg → NED2) reads in order, but predicate / elicitation batches can sit in a different wave.

Step Stage Batch ID Status When
creating Elicitation batch_69a251b54ea88190b18281669f59b4c0 completed Feb. 28, 2026, 2:23 a.m.
NER Named-entity recognition batch_69a2573e4e6481908252dfef2e34f46e completed Feb. 28, 2026, 2:47 a.m.
NED1 Entity disambiguation (via context triple) batch_69a2a3d5c7bc8190ba8b36db41a1a57f completed Feb. 28, 2026, 8:14 a.m.
NEDg Description generation batch_69a2a4f0e7c081908966789fd07e59a2 completed Feb. 28, 2026, 8:18 a.m.
NED2 Entity disambiguation (via description) batch_69a2a58757d081908c7c5469c485f1cc completed Feb. 28, 2026, 8:21 a.m.
Created at: Feb. 28, 2026, 2:27 a.m.