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.
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
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The barber shaves no one who shaves himself → |
| basedOn |
Russell's paradox
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|
| category |
paradoxes of self-reference
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semantic and logical paradoxes → |
| demonstrates |
inconsistency of the defining condition for the barber
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paradox arising from self-application of a rule → |
| expressedIn |
natural language
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|
| 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
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to show how paradoxes can arise from everyday descriptions → |
| hasDomain |
village of people and a barber
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|
| hasFormulation |
There is a barber who shaves all and only those who do not shave themselves
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|
| hasKeyQuestion |
Does the barber shave himself?
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|
| hasRole |
barber who shaves certain people
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|
| hasStructure |
self-membership analogue in everyday language
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|
| 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
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logical consistency → membership conditions → self-shaving → |
| leadsTo |
contradiction when asking whether the barber shaves himself
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|
| relatedTo |
Russell's paradox
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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
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|
| shows |
need for restrictions on set or property formation
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not every description determines a possible object → some apparently simple conditions are inconsistent → |
| usedIn |
introductory logic teaching
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philosophy education → popular explanations of Russell's paradox → |
Referenced by (2)
| Subject (surface form when different) | Predicate |
|---|---|
|
Epimenides paradox
→
Russell’s paradox → |
relatedTo |