naive set theory
E361579
Naive set theory is an early, intuitive approach to set theory that treats any definable collection as a set, but is known to be inconsistent due to paradoxes such as Russell’s and Curry’s.
All labels observed (2)
| Label | Occurrences |
|---|---|
| naive set theory canonical | 3 |
| Naive Set Theory | 1 |
How this entity was disambiguated
This entity first appeared as the object of triple T3478144 — 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: naive set theory Context triple: [Curry paradox, arisesIn, naive set theory]
-
A.
set theory
Set theory is a foundational branch of mathematical logic that studies collections of objects, called sets, and underpins much of modern mathematics.
-
B.
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.
-
C.
Zermelo set theory
Zermelo set theory is an early axiomatic system for set theory, introduced by Ernst Zermelo to rigorously formalize the concept of sets and avoid known paradoxes.
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D.
von Neumann universe
The von Neumann universe is a cumulative, well-founded hierarchy of sets used as a standard model of the set-theoretic universe in axiomatic set theory.
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E.
von Neumann–Bernays–Gödel set theory
Von Neumann–Bernays–Gödel set theory is an axiomatic set theory extending Zermelo–Fraenkel set theory by formally distinguishing between sets and classes, widely used in foundational studies of mathematics.
- 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: naive set theory Target entity description: Naive set theory is an early, intuitive approach to set theory that treats any definable collection as a set, but is known to be inconsistent due to paradoxes such as Russell’s and Curry’s.
-
A.
set theory
Set theory is a foundational branch of mathematical logic that studies collections of objects, called sets, and underpins much of modern mathematics.
-
B.
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.
-
C.
Zermelo set theory
Zermelo set theory is an early axiomatic system for set theory, introduced by Ernst Zermelo to rigorously formalize the concept of sets and avoid known paradoxes.
-
D.
von Neumann universe
The von Neumann universe is a cumulative, well-founded hierarchy of sets used as a standard model of the set-theoretic universe in axiomatic set theory.
-
E.
von Neumann–Bernays–Gödel set theory
Von Neumann–Bernays–Gödel set theory is an axiomatic set theory extending Zermelo–Fraenkel set theory by formally distinguishing between sets and classes, widely used in foundational studies of mathematics.
- F. None of above. chosen
Statements (48)
| Predicate | Object |
|---|---|
| instanceOf |
foundational theory of mathematics
ⓘ
mathematical theory ⓘ set theory ⓘ |
| allows | unrestricted comprehension ⓘ |
| assumes | for any property there exists a set of all objects having that property ⓘ |
| basedOn | intuitive notion of collection ⓘ |
| contradicts | classical logic when combined with unrestricted comprehension ⓘ |
| formalismIncludes |
membership relation
ⓘ
set-builder notation ⓘ |
| hasAlternativeName | informal set theory ⓘ |
| hasFeature |
informal reasoning about membership
ⓘ
no distinction between sets and proper classes ⓘ unrestricted formation of subsets by properties ⓘ |
| hasGoal | provide a simple basis for talking about collections in mathematics ⓘ |
| historicallyPreceded | axiomatic set theory ⓘ |
| influenced |
Zermelo set theory
ⓘ
Zermelo–Fraenkel set theory ⓘ class theory ⓘ development of axiomatic set theories ⓘ type theory ⓘ |
| isContrastedWith |
New Foundations for Mathematical Logic
ⓘ
surface form:
Quine's New Foundations
Zermelo–Fraenkel set theory ⓘ axiomatic set theory ⓘ von Neumann–Bernays–Gödel set theory ⓘ |
| isDiscussedIn |
foundations of mathematics literature
ⓘ
introductory logic textbooks ⓘ |
| isInconsistentBecauseOf |
Burali-Forti paradox
ⓘ
Cantor’s paradox ⓘ
surface form:
Cantor's paradox
Curry paradox ⓘ
surface form:
Curry's paradox
Russell’s paradox ⓘ
surface form:
Russell's paradox
|
| isKnownFor |
intuitive appeal
ⓘ
logical inconsistency ⓘ simplicity ⓘ |
| isRelatedTo |
Frege’s system in "Grundgesetze der Arithmetik"
ⓘ
surface form:
Frege's Basic Law V
Frege’s system in "Grundgesetze der Arithmetik" ⓘ
surface form:
Frege's system in Grundgesetze der Arithmetik
|
| isUsedFor | motivating axiomatic restrictions in modern set theory ⓘ |
| isUsedIn |
informal mathematical practice
ⓘ
introductory expositions of set theory ⓘ |
| leadsTo | self-referential definitions of sets ⓘ |
| motivated |
distinction between sets and proper classes
ⓘ
introduction of replacement axiom ⓘ introduction of separation axiom ⓘ |
| permits |
set of all sets
ⓘ
set of all sets that do not contain themselves ⓘ |
| treatsAsSet |
any collection of objects satisfying a property
ⓘ
any definable collection ⓘ |
| usesPrinciple | comprehension schema ⓘ |
| wasUnderminedBy | Russell's discovery of his paradox ⓘ |
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: naive set theory Description of subject: Naive set theory is an early, intuitive approach to set theory that treats any definable collection as a set, but is known to be inconsistent due to paradoxes such as Russell’s and Curry’s.
Referenced by (4)
Full triples — surface form annotated when it differs from this entity's canonical label.
this entity surface form:
Naive Set Theory