Curry paradox
E73424
Curry paradox is a self-referential logical paradox that arises in certain formal systems without using negation, showing how naive reasoning about implication and self-reference can lead to triviality.
All labels observed (4)
| Label | Occurrences |
|---|---|
| Curry’s paradox | 3 |
| Curry paradox canonical | 1 |
| Curry's paradox | 1 |
| Horned man paradox | 1 |
How this entity was disambiguated
This entity first appeared as the object of triple T568427 — 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: Curry paradox Context triple: [liar paradox, relatedTo, Curry paradox]
-
A.
Berry paradox
The Berry paradox is a self-referential logical paradox arising from phrases like “the smallest positive integer not definable in under eleven words,” which appears to define exactly such a number while claiming it cannot be defined.
-
B.
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.
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C.
Epimenides paradox
The Epimenides paradox is a classic self-referential logical puzzle arising from a Cretan philosopher’s claim that all Cretans are liars, illustrating the problem of statements that refer to their own truth or falsehood.
-
D.
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.
-
E.
liar paradox
The liar paradox is a classic self-referential logical puzzle arising from sentences that declare their own falsehood, leading to a contradiction about whether they are true or false.
- 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: Curry paradox Target entity description: Curry paradox is a self-referential logical paradox that arises in certain formal systems without using negation, showing how naive reasoning about implication and self-reference can lead to triviality.
-
A.
Berry paradox
The Berry paradox is a self-referential logical paradox arising from phrases like “the smallest positive integer not definable in under eleven words,” which appears to define exactly such a number while claiming it cannot be defined.
-
B.
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.
-
C.
Epimenides paradox
The Epimenides paradox is a classic self-referential logical puzzle arising from a Cretan philosopher’s claim that all Cretans are liars, illustrating the problem of statements that refer to their own truth or falsehood.
-
D.
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.
-
E.
liar paradox
The liar paradox is a classic self-referential logical puzzle arising from sentences that declare their own falsehood, leading to a contradiction about whether they are true or false.
- F. None of above. chosen
Statements (45)
| Predicate | Object |
|---|---|
| instanceOf |
logical paradox
ⓘ
self-referential paradox ⓘ semantic paradox ⓘ |
| arisesIn |
certain formal systems with contraction
ⓘ
naive set theory ⓘ naive truth theory ⓘ systems with unrestricted modus ponens ⓘ unrestricted comprehension schemas ⓘ |
| canBeBlockedBy |
rejecting contraction
ⓘ
restricting conditional proof ⓘ restricting modus ponens ⓘ using non-classical conditionals ⓘ |
| canLeadTo |
explosion of the theory
ⓘ
triviality ⓘ |
| doesNotRequire |
falsity predicate
ⓘ
negation ⓘ |
| hasAlternativeName |
Curry paradox
ⓘ
surface form:
Curry’s paradox
|
| hasConsequence | collapse of a theory into proving every sentence ⓘ |
| hasForm | self-referential sentence implying an arbitrary statement ⓘ |
| historicallyAttributedTo | Haskell Curry ⓘ |
| involves |
conditional proof
ⓘ
material implication ⓘ naive reasoning about implication ⓘ self-reference ⓘ |
| isAnalogousTo |
Russell’s paradox
ⓘ
surface form:
Russell paradox
|
| isDiscussedIn |
foundations of mathematics
ⓘ
philosophical logic ⓘ theories of truth ⓘ |
| isRelatedTo |
liar paradox
ⓘ
surface form:
Liar paradox
paradoxes of entailment ⓘ paradoxes of material implication ⓘ |
| isUsedAs |
argument against naive truth definitions
ⓘ
example of self-referential inconsistency ⓘ test case for non-classical logics ⓘ |
| motivates |
non-classical logics
ⓘ
paraconsistent logics ⓘ restrictions on structural rules ⓘ substructural logics ⓘ |
| namedAfter | Haskell Curry ⓘ |
| requires | a conditional that validates certain structural rules ⓘ |
| shows |
dangers of unrestricted self-reference
ⓘ
inconsistency of naive reasoning about implication ⓘ |
| threatens |
naive set-theoretic comprehension
ⓘ
systems with naive truth predicates ⓘ |
| typicalConstruction | a sentence that asserts: if this sentence is true, then φ ⓘ |
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: Curry paradox Description of subject: Curry paradox is a self-referential logical paradox that arises in certain formal systems without using negation, showing how naive reasoning about implication and self-reference can lead to triviality.
Referenced by (6)
Full triples — surface form annotated when it differs from this entity's canonical label.
this entity surface form:
Curry’s paradox
this entity surface form:
Horned man paradox
this entity surface form:
Curry’s paradox
this entity surface form:
Curry’s paradox
this entity surface form:
Curry's paradox