Yablo's paradox: Difference between revisions
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The paradox arises from considering the following infinite set of sentences: |
The paradox arises from considering the following infinite set of sentences: |
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* (S1): for all k >1, Sk is false |
* (S1): for all k >=1, Sk is false |
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* (S2): for all k >2, Sk is false |
* (S2): for all k >=2, Sk is false |
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* (S3): for all k >3, Sk is false |
* (S3): for all k >=3, Sk is false |
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* ... |
* ... |
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* ... |
* ... |
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Revision as of 08:17, 17 January 2010
Yablo's paradox is a liar-like paradox without any apparent self-reference published by Stephen Yablo in 1993.
The paradox
The paradox arises from considering the following infinite set of sentences:
- (S1): for all k >=1, Sk is false
- (S2): for all k >=2, Sk is false
- (S3): for all k >=3, Sk is false
- ...
- ...
The set is paradoxical, because it is unsatisfiable (contradictory), but this unsatisfiability defies immediate intuition.
Moreover, none of the sentences refers to itself, but only to the subsequent sentences; and this leads Yablo to claim that his liar-like paradox does not rely on self-reference.
External links
- "Paradox Without Self-Reference" - Analysis, vol. 53 (1993), pp. 251–52