The sorites paradox shows that vague words like 'heap' seem to lead from true premises to an absurd conclusion. Philosophers disagree about where the reasoning fails.
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The liar paradox arises from a sentence like "This sentence is false," which seems to be true only if it is false and false only if it is true. Experts still disagree on how to resolve it.
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Russell's paradox shows that the set of all sets that are not members of themselves cannot exist. It exposed a contradiction in naive set theory and prompted new foundations for mathematics.
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