Barber paradox

E13607

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.


Statements (47)
Predicate Object
instanceOf illustration of Russell's paradox
logical paradox
philosophical puzzle
self-referential paradox
thought experiment
assumes The barber shaves all those who do not shave themselves
The barber shaves no one who shaves himself
basedOn Russell's paradox
category paradoxes of self-reference
semantic and logical paradoxes
demonstrates inconsistency of the defining condition for the barber
paradox arising from self-application of a rule
expressedIn natural language
formalizableAs question whether the barber is a member of that set
set of all people in the village who do not shave themselves
hasDidacticPurpose to make Russell's paradox more intuitive
to show how paradoxes can arise from everyday descriptions
hasDomain village of people and a barber
hasFormulation There is a barber who shaves all and only those who do not shave themselves
hasKeyQuestion Does the barber shave himself?
hasRole barber who shaves certain people
hasStructure self-membership analogue in everyday language
illustrates Russell's paradox
limits of naive set theory
logical contradiction
problems with unrestricted comprehension
self-reference problem
set-theoretic inconsistency
involvesConcept existence of objects satisfying given conditions
logical consistency
membership conditions
self-shaving
leadsTo contradiction when asking whether the barber shaves himself
relatedTo Russell's paradox
foundations of mathematics
liar paradox
naive set theory
philosophy of logic
self-referential definitions
set of all sets that do not contain themselves
resolution no such barber can exist under the given conditions
shows need for restrictions on set or property formation
not every description determines a possible object
some apparently simple conditions are inconsistent
usedIn introductory logic teaching
philosophy education
popular explanations of Russell's paradox

Referenced by (2)
Subject (surface form when different) Predicate
Epimenides paradox
Russell’s paradox
relatedTo

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