Barber paradox
E13607
illustration of Russell's paradox
logical paradox
philosophical puzzle
self-referential paradox
thought experiment
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.
All labels observed (1)
| Label | Occurrences |
|---|---|
| Barber paradox canonical | 2 |
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
ⓘ
surface form:
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
ⓘ
surface form:
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
ⓘ
surface form:
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)
Full triples — surface form annotated when it differs from this entity's canonical label.