Kleene–Rosser paradox

E943473

logical paradox result in mathematical logic semantic paradox

The Kleene–Rosser paradox is a logical contradiction in untyped lambda calculus that demonstrated the inconsistency of Alonzo Church’s original formulation of the system.

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All labels observed (2)

Label	Occurrences
Kleene–Rosser paradox canonical	1
Kleene–Rosser paradox in lambda calculus	1

Statements (47)

Predicate	Object
instanceOf	logical paradox ⓘ result in mathematical logic ⓘ semantic paradox ⓘ
appliesTo	original formulation of Church’s lambda calculus ⓘ untyped lambda calculus ⓘ
concerns	beta-reduction properties ⓘ equational reasoning in lambda calculus ⓘ impredicative definitions in lambda calculus ⓘ unrestricted lambda abstraction ⓘ
contradicts	consistency of Church’s original system ⓘ
demonstrates	existence of a lambda term leading to contradiction ⓘ limits of naive formalization of functions ⓘ
describes	logical contradiction in untyped lambda calculus ⓘ
field	foundations of mathematics ⓘ lambda calculus NERFINISHED ⓘ mathematical logic ⓘ proof theory ⓘ
formalism	lambda calculus notation ⓘ
hasConsequence	original untyped system is inconsistent with certain logical principles ⓘ
hasDomain	formal systems ⓘ theory of computation ⓘ
historicalPeriod	1930s ⓘ
impact	influenced later work on consistency of formal systems ⓘ led to modification of Church’s original system ⓘ
involves	construction of a term that asserts its own non-terminating behavior ⓘ
isDiscussedIn	historical studies of Church’s lambda calculus ⓘ literature on lambda calculus foundations ⓘ texts on computability theory ⓘ
isExampleOf	paradox arising from unrestricted abstraction ⓘ self-referential construction in logic ⓘ
motivated	development of consistent typed lambda calculi ⓘ restrictions on abstraction in lambda calculus ⓘ revisions of Church’s original system ⓘ
namedAfter	J. Barkley Rosser NERFINISHED ⓘ Stephen Cole Kleene NERFINISHED ⓘ
relatedTo	Church’s lambda calculus NERFINISHED ⓘ Church’s thesis NERFINISHED ⓘ Curry’s paradox NERFINISHED ⓘ Russell’s paradox NERFINISHED ⓘ combinatory logic ⓘ inconsistency proofs ⓘ liar paradox ⓘ typed lambda calculus ⓘ
shows	danger of unrestricted self-application in formal systems ⓘ inconsistency of Church’s original lambda calculus ⓘ
uses	diagonalization technique ⓘ self-referential lambda terms ⓘ

Referenced by (2)

Full triples — surface form annotated when it differs from this entity's canonical label.

Barkley Rosser → notableWork → Kleene–Rosser paradox ⓘ

Barkley Rosser → notableConcept → Kleene–Rosser paradox ⓘ

this entity surface form: Kleene–Rosser paradox in lambda calculus