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.
Aliases (2)
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’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 paradox
→
|
| isDiscussedIn |
foundations of mathematics
→
philosophical logic → theories of truth → |
| isRelatedTo |
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
→
|
Referenced by (3)
| Subject (surface form when different) | Predicate |
|---|---|
|
Curry paradox
("Curry’s paradox")
→
|
hasAlternativeName |
|
Eubulides of Miletus
("Horned man paradox")
→
|
knownFor |
|
liar paradox
→
|
relatedTo |